Home

GLoBES GLoBES

1. 8 000 t GW yr 6 B Beams In preparation Table 2 1 Pre defined experiment prototypes their filenames to be used in glbInitExperiment their short descriptions and the references in which they are originally used and discussed except from minor modifications such as a different implementation of the energy threshold function Note that some of these experiments are outdated in terms of integrated luminosities baseline fluxes efficiencies or other factors In any case these file are installed along with GLoBES 16 CHAPTER 2 GLoBES basics In principle the GLoBES user interface can currently handle up to 32 of different long baseline experiments simultaneously where the number of existing experiment definition files can of course be unlimited This means that their Ay values are added after the minimization over the systematics parameters and before any minimization over the os cillation parameters Note that each experiment assumes a specific matter density profile which means that it makes sense to simulate different operation modes within one exper iment definition and physically different baselines in different definitions For details of the rate computation and simulation techniques we refer at this place to Part II Though the simplest case of simulating one experiment may be most often used using more than one experiments are useful in many cases For example combinations of experiments can be tested for complement
2. sampling stepsize 1 0 2 0 3 0 4 0 5 0 76 CHAPTER 9 Experiment definition with AEDL The choice of the sampling point configuration strongly depends on the experiment and required accuracy Ideally the integrand of Eq 9 9 is zero outside the sampling range if this cannot be achieved it is usually sufficient that the sampling range is by about three times the energy resolution larger than the bin range The spacing of the sampling points should be somewhat smaller a factor gt 2 usually is more than ebough than the finest details of the integrand Bin level This level is determined by the experiment and its analysis Note that energy bin sizes much smaller than the energy resolution will not improve the results The energy bin range and the number of energy bins do always have to be specified For the case of large values of the integrand in Eq 9 9 at the energy range limits it is recommended to exceed the analysis energy window by about three times the energy calibration error in order to avoid cutoff effects In order to define a range between Emin and Emax divided by a certain number of equidistant bins use emin 4 0 emax 50 0 bins 20 For arbitrary bins use Emin and Emax and the size of each bin AB emin 4 0 emax 50 0 binsize 15 0 5 0 20 0 6 0 The number of bins will be automatically computed by GLoBES Note that the bin sizes have to add up to the energy range emax emin The choic
3. sin 20 3 CHAPTER 5 Locating degenerate solutions 41 manifold shown in the figure on page 40 therefore do not appear at the same oscillation parameter values except from the ones shown in the figure For the more advanced reader a number of tricks can be useful for the numerical localization of degenerate solutions Minimum x larger than threshold If a located degeneracy has a minimum x larger than the corresponding confidence level threshold for the discussed quantity of in terest the degeneracy can be immediately ignored This saves a lot of computation time Locating degeneracies in more complicated topologies For more complicated topologies such as for neutrino factories it is often useful to use multi step location procedures or analytical knowledge For example for a numerical procedure one may first of all switch off the systematics and keep sin 2013 or dcp fixed i e use glbChiTheta where sin 2013 or dcp is fixed at the best fit value The result can then be used as a starting point for glbChiAll for the individual experiments with the systematics switched on again Forcing the minimizer into the targeted solution In addition to switching off the systematics it can be useful to reduce the input errors during some steps of the localization process in order to make the minimizer not to run away too much from the targeted solution The example on page 40 illustrates this with the input error for Am3 Since t
4. Ile res na dy a eh sec N EN Aa 118 How to use this manual As it is illustrated in Fig 1 GLoBES consists of several modules AEDL Abstract Exper GLoBES User Interface C library which loads AEDL file s and provides functions to simulate experiment s Tee eee eee eee nn nn m m ad Figure 1 Different modules in GLoBES iment Definition Language is a language to define experiments in form of ordinary text files One or more of the resulting AEDL files can then be processed together with support ing flux or cross section files by the user interface The user interface is a C library which loads one or more AEDL file s containing the experiment definition s The user interface is linked against the application software and provides the user interface functions for the intended experiment simulation The application software is except from some example files not part of GLoBES since the evaluation of the experiment performance is often a matter of taste and definition In addition the algorithms depend especially for high precision instruments very much on the oscillation parameters In general it is quite simple to simulate superbeams and reactor experiments However because of the more complicated topology the simulation of neutrino factories is much more difficult In order to demonstrate some of these difficulties we present in this manual only examples with neutrino factories These examples can be 2 CONTEN
5. VI CONTENTS 7 4 Algorithm parameters Filter functions 0 53 II The Abstract Experiment Definition Language AEDL 55 8 Getting started 57 8 1 General concept of the experiment simulation 57 8 2 A simple example for AEDL 14 40 s we Sr zu er Eee bs 61 8 3 Introduction to the syntax of AEDL 2 nenn 64 9 Experiment definition with AEDL 67 9 1 Source properties and integrated luminosity 2 2 222 nn 67 9 2 Baseline and matter density profile 2 2 22 nn nenn 69 0 37 BLOSS SECTIONS ew gs a a wees A Sod ya Te ae eS 70 9 4 Osallation channels u ae as 21 a Et a a rasen 71 9 5 Energy resolution function aa zen are a 74 9 5 1 Introduction and principles 2 22 2 En nn 74 9 5 2 Bin based automatic energy smearing TT 9 5 3 Low pass filter 2 28 Ha seen Bar ee 79 9 5 4 Manual energy smearing rs a Bag a 80 9 6 Rules and the treatment of systematics aooo a 81 9 7 Version control in AEDL files 4 ee ee a 85 10 Testing amp debugging of AEDL files 87 10 1 Basic usage of the globes binary au Eier Er ee ee 87 10 2 Testing AEDL files a aaa a 88 Acknowledgments 91 GLoBES installation 93 The GNU General Public License 99 GNU Free Documentation License 105 Bibliography 109 Indices 113 APL functions ot eaa w ere Dr a ai iR BPE A amp we Si ee we 114 API constants amp maclose are Br er preis per 116 ABDEfBlerente wer a a PERS Pe Oe OSS 117
6. filter_state is ignored whenever a density profile with more than one layer is used With a type 1 type 1 energy resolution function ce adds on to the energy reso lution function of the detector o E such as On EL 0 0 E 9 16 Sometimes this behavior is unwanted and therefore one can try to subtract the filtering from the energy resolution function by splitting the energy resolution function o E g in two parts by Cal EY oE 02 02 9 17 52 E where the truncated energy resolution function 9 E is used instead of o E in computing the smearing data Thus one obtains as effective energy resolution ogl EY oE 9 18 This scheme is used by choosing as type for the energy resolution type 2 9 5 4 Manual energy smearing In some cases one may use the output of a detector Monte Carlo simulation directly Then one can use manual energy smearing instead of the automatic energy smearing algorithms The energy smearing matrix K has bins rows and sampling_points columns which are numbered from 0 to bins 1 or sampling_points 1 It is equivalent to the bin and sampling point based kernel in Eq 9 8 where F is the energy of the jth sampling point In general many of the entries in this matrix are zero which means that it is convenient to evaluate the integrand in Eq 9 9 only at positions where Kj is non zero The corresponding sampling range range of non zero
7. 69 log 66 logi0 66 NEXT 65 profiletype 69 sampling_max 75 sampling_min 75 sampling_points 75 sampling_stepsize 75 sin 66 sqrt 66 tan 66 target_mass 68 version 85 118 Index Advanced tricks 31 41 AEDL 54 85 external parameters 52 65 names 43 Aliasing 79 Auxiliary parameter 25 Background centers 50 errors 50 Bar plots 51 Baseline 69 change 47 Bin 73 Build process see Compilation C Code 14 Channel 59 71 Compilation of application programs 13 Correlation and Ax 27 multi parameter 27 32 two parameter 24 32 Cross section 46 70 file 71 comments in 71 Degeneracies 39 41 and Ax 39 multiple solutions 39 sgn Am3 degeneracy 40 Detector mass 18 Energy resolution 72 74 81 resolution function 78 window 83 Environment variables GLB_CENTRAL_VALUES 88 GLB_PATH 17 CHAPTER Indices Error dimension 50 84 Event rates 44 Examples 13 Experiment delete 17 list 16 clear 17 number of 16 Experiment files table 15 Experiment initialization 16 Experiment parameters 47 External information 29 input errors 29 30 precision 30 priors 29 31 starting values 29 30 External input see External information File names 65 Filter 79 functions 53 Flux 46 file 69 comments in 69 GLB_ALL 16 GLB_CENTRAL_VALUES 88 glb files 15 glb files installation 13 94 GLB_PATH 17 globes 87 channel rates
8. E D Pz z In order to access fluxes at arbitrary energies linear interpolation is used by the software In general it is advisable to provide the flux between sampling_min and sampling_max cf Sec 9 5 since these values are used by the software However if the energy leaves the range of values given in the file zero is returned The the columns for the fluxes for unused flavours have to be filled all the same e g with zeros The flux files accept one line comments which start with and end with the linefeed character n they are not counted as a line and their content is discarded This comments are useful to provide meta information about the fluxes like units or the origin of the information This is also the default method to point the user to the references he she should to cite when using a particular flux 9 2 Baseline and matter density profile The baseline and matter density profile determine besides energy and involved flavors the neutrino oscillation physics at the experiment description level All of the neutrino oscillation parameters are defined at running time The baseline is given by baseline 3000 0 Note that baseline lengths are always assumed to be in kilometers Furthermore the matter density profile along the baseline has to be specified The simplest matter density profile is a constant matter density profile with the average matter density from the PREM 2 onion shell mode
9. The oscillation parameters all density values and the number of iterations are printed as pretty output Use stdout for stream if you want to print to the screen In addition to these basic functions there are functions to access the individual parameters within the parameter vectors Function 2 15 glb_params glbSetOscParams glb_params in double osc int which sets the oscillation parameter which in the structure in to the value osc If the assignment was unsuccessful the function returns NULL Function 2 16 double glbGetOscParams glb_params in int which returns the value of the oscillation parameter which in the structure in In both of these functions the parameter which runs from 0 to 5 where the parameters in GLoBES always have the order 61 613 23 dcp Am3 Am3 Alternatively to the number the constants GLB_THETA_12 GLB_THETA_13 GLB_THETA_23 GLB_DELTA_CP GLB_DM_SOL or GLB_DM_ATM can be used Similarly the density parameters or number of iterations returned by the minimizers can be accessed Function 2 17 glb_params glbSetDensityParams glb_params in double dens int which sets the density parameter which in the structure in to the value dens If the assignment was unsuccessful the function returns NULL If GLB_ALL is used for which the density parameters of all experiments will be set accordingly 2 4 Computing the simulated data 21 Function 2 18 double glbGetDensityParams glb_params in int which returns
10. This we would obtain from the first appearance channel only chi2 glbChiSys fit_values 0 0 fprintf stream This we would have from the CP even appearance channel only g n n chi2 Output 6 CHAPTER 1 A GLoBES tour This we would have from the CP even appearance channel only 21 6223 The sum over all rules again gives chi2 glbChiSys fit_values GLB_ALL 0 glbChiSys fit_values GLB_ALL 1 glbChiSys fit_values GLB_ALL 2 glbChiSys fit_values GLB_ALL 3 fprintf stream The sum over all rules gives again g n n chi2 Output The sum over all rules gives again 22 3984 Let s prepare the minimizers for taking into account correlations Set errors for external parameters too 10 for each of the solar parameters and 5 for the matter density glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues true_values glbSetInputErrors input_errors Then we can calculate x including the full multi parameter correlation and show where GLoBES actually found the minimum note that this takes somewhat longer than system atics only This corresponds to a projection onto the sin 20 3 axis chi2 glbChiTheta fit_values minimum GLB_ALL fprintf stream chi2 with correlations g n chi2 fprintf stream Position of minimum thetai2 theta13 theta23 delta sdm ldm rho n glbPrintParams stream minimum fprintf stream Note tha
11. and d x Vx R 2xRcos is the purely geometrical relationship between d and x with the Earth radius R and the nadir angle cos 0 L 2R p L 5 IH rat ae 7 4 Function 7 7 int glbGetProfileDatalInExperiment int exp size_t layers double lengths double densities returns the matter density profile currently used for experiment exp The number of layers layers the list of lengths lengths and the list of densities densities are returned All these functions return 1 if they were not successful The counterpart of these functions to assign a specific matter density profile to an experiment is Function 7 8 int glbSetProfileDataInExperiment int exp size_t layers const double lengths const double densities sets the matter density of experiment exp to an arbitrary profile with layers steps The density layers are specified by the lists lengths and densities The function returns 1 if it was not successful Note that this function requires that the memory space for the lists be reserved already Finally let us take a look at two examples This example changes the baseline length to 7500 km where the average matter density is manually computed double lengths double densities glbAverageDensityProfile 7500 amp lengths amp densities glbSetProfileDataInExperiment 0 1 lengths densities free lengths free densities In the second example we change the baseline to a PREM profile wit
12. for the number of signal components or GLB_BG for the number of background components 6 3 Event rates 45 Function 6 9 double glbGetNormalizationInRule int exp int rule int signal returns the normalization normalization or background center in rule rule of the experiment exp The parameter signal refers to signal GLB_SIG or background GLB_BG Function 6 10 int glbGetChannelInRule int exp int rule int pos int signal returns the channel number in rule rule at the position pos of the experi ment exp The parameter signal refers to signal GLB_SIG or background GLB_BG Function 6 11 double glbGetCoefficientInRule int exp int rule int pos int signal returns the coefficient of the component pos in rule rule of the experiment exp The parameter signal refers to signal GLB_SIG or background GLB_BG In addition GLoBES has channel based rate functions Function 6 12 int glbShowChannelRates FILE stream int exp int channel int smearing int effi int bgi prints the binned channel rates as list with energy and event rate to the file stream either an open file or stdout A specific experiment exp and a specific channel channel have to be chosen The function may return the rates before GLB_PRE or after GLB_POST the energy smearing as it is specified by smearing In addition it may contain the pre and post smearing efficiencies set effi to GLB_W_EFF or GLB_WO_EFF and the pre and post smearing backgrounds set bgi
13. possibilities are shown in Table 9 2 Since the error dimension defines the treatement of systematics it is useful to have define a matched pair of error dimensions for each rule where on value describes how the event rate is computed for no systematics and the other one is with systematics see also Sec 7 2 The error dimensions for the case of no systematics is set for each rule by the value of errordim_sys_off whereas the error dimension for systematics on is given by errordim_sys_on Thus for example the complete error dimension definition could look like errordim_sys_off 2 errordim_sys_on 0 It is foreseen to add the possiblity to extend the set of error dimensions or the set of possible systematical errors in one of the next versions of GLoBES Eventually a rule looks like rule rule_1 lt signal 0 5 channel_1 background 0 001 channel_2 0 005 channel_3 9 7 Version control in AEDL files 85 a 5 ed Tik Calibration Systematics with tilt No systematics Total rates Spectrum only Total rates No systematics Systematics with calibration Table 9 2 Possible values of the error dimensions variable in GLoBES and their meaning If a parameter is designated with it will be marginalized over and therefore the corresponding error needs to have a non zero value If the cases with total rates in the remarks the summation over the bins is performed before computing the x i
14. 4 1 Left plot The correlation between sin 2913 and dcp as calculated in the example on page 24 but for 1 d o f only Right plot The x value of the projection onto the sin 26 3 axis as function of sin 2913 The projection onto the sin 26 3 axis is obtained by finding the minimum x value for each fixed value of sin 2913 in the left hand plot i e along the gray vertical lines The thick gray curve marks the position of these minima in the left hand plot The arrows mark the obtained fit ranges for sin 2013 at the 30 confidence level 1 d o f i e the precision of sin 2013 The following functions are some of the simplest minimizers provided by GLoBES Function 4 5 double glbChiTheta const glb_params in glb_params out int exp returns the projected x onto the 013 axis for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all parameters other than 013 and the fixed fit value of 013 The actually determined parameters at the minimum are returned in out where 013 is still at its fixed value If out is set to NULL this information will not be returned Function 4 6 double glbChiDelta const glb_params in glb_params out int exp returns the projected x onto the dcp azis for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all
15. INABILITY TO USE THE PROGRAM INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED CHAPTER The GNU General Public License 103 INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES END OF TERMS AND CONDITIONS 104 CHAPTER The GNU General Public License 105 GNU Free Documentation License Version 1 2 November 2002 Copyright 2000 2001 2002 Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The purpose of this License is to make a manual textbook or other functional and useful document free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secondarily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to
16. a site script 98 CHAPTER GLoBES installation 99 The GNU General Public License Version 2 June 1991 Copyright 1989 1991 Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed Preamble The licenses for most software are designed to take away your freedom to share and change it By contrast the GNU General Public License is intended to guarantee your freedom to share and change free software to make sure the software is free for all its users This General Public License applies to most of the Free Software Foundation s software and to any other program whose authors commit to using it Some other Free Software Foundation software is covered by the GNU Library General Public License instead You can apply it to your programs too When we speak of free software we are referring to freedom not price Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software and charge for this service if you wish that you receive source code or can get it if you want it that you can change the software or use pieces of it in new free programs and that you know you can do these things To protect your rights we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights These
17. a very sophisticated application software to find all degenerate solutions The function to perform the all parameter minimization is glbChiAll Function 5 1 double glbChiAll const glb_params in glb_params out int exp returns the minimized x over all parameters for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer The actually determined parameters at the minimum are returned in out If out is set to NULL this information will not be returned This function takes the suspected position of the local minimum and returns its actual position in out as well as the y value at the minimum as return value Thus the return value can be immediately used to judge whether the located degeneracy appears at the chosen confidence level The example on page 40 illustrates how to locate the sgn Am3 degeneracy and show the corresponding degenerate solution in the sin 2013 cp plane together with the original solution In this case the position of the degeneracy can be easily guessed to be at the true parameter values but with inverted Am3 The minimizer then runs off the plane of these parameters into the local minimum It is very important to take into account the position of the degeneracy off this plane since the actual x in the minimum is probably lower than in the plane Thus the degeneracy may not even appear at the chosen confidence level
18. algorithm is for example energy name lt type 1 sigma_function standard sigma_e 0 15 0 0 0 0 9 5 3 Low pass filter In order to ensure that fast oscillating probabilities do not lead to aliasing it is possible to impose a low pass filter already during the calculation of the probabilities itself This filter is implemented has a highly experimental feature called filter The calculation of oscillation probabilities is in principle a computation of phase differences Restricting the maximum admissible size of those phase differences effectively filters the high frequency component of the oscillation probability This idea is implemented according to Pag E gt UU U U 4 xe a 9 14 aj where Am L 2E is the usual phase difference and the last term is a Gau ian filter with width o E Choosing o E o E ensures that this filter behaves approximately such as an energy resolution function with constant width oe V2 oF ie 1 db P ar 9 15 e 206 P Oe V2T The relationship between Eqs 9 14 and 9 15 is not obvious and connected to the properties of Pag see Refs 10 11 This feature works only for vacuum and constant densities and is controlled by the filer state variable In addition o is set by the filter value variable filter_state 1 filter_value 2 0 80 CHAPTER 9 Experiment definition with AEDL would switch the filter feature on and set the width to 2 0GeV The setting of
19. and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an otherwise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Transparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCII without markup Texinfo in put format LaTeX input format SGML or XML using a publicly available DTD and standard conforming simple HTML PostScript or PDF designed for human modification Examples of transparent image for mats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and edited only by proprietary word processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plus such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of
20. and the experiment counter is increased The experiment then has the number glb_num_of_exps 1 The elements of the experiment list have the type glb_exp which the user will not need to access directly in most cases The experiment definition files which usually end with glb and any supporting files are first of all searched in the current directory and then in the path given in the environment variable GLB_PATH A list of pre defined experiment prototypes their filenames their short descriptions and the references of their definitions can be found in Table 2 1 If the program cannot find these files or some of them are syntactically not correct it will break at this place One can also remove all experiments from the evaluation list at running time Function 2 3 void glbClearExperimentList removes all experiments from the inter nal list and resets all counters Note that changing the number of experiments requires a new initialization of all parame ters of the types glb_params and glb_projection if the number of experiments changes since these parameter structures internally carry lists for the matter densities of all experi ments Similarly once should never call glbAlloc before the experiment initialization 18 CHAPTER 2 GLoBES basics 2 2 Units in GLoBES and the integrated luminosity While interacting with the user interface of GLoBES parameters are transferred to and from the GLoBES library In GLoBES one set of units
21. as explained below Function 7 2 int glbSetBaselineInExperiment int exp double baseline sets the baseline length in experiment exp to baseline The function returns 1 if it was not successful 48 CHAPTER 7 Changing experiment parameters at running time Note that glbSetBaselineInExperiment does not change the profile type in the experi ment The counterpart of this function is Function 7 3 double glbGetBaselineInExperiment int exp returns the baseline length currently used for experiment exp One can not change the profile type of an experiment manually during running time However one can change the matter density profile where the profile type is automatically changed to 3 i e arbitrary matter density profile In addition a number of functions are provided to compute possible matter density profiles average density PREM profile In general a matter density profile in GLoBES with N layers is represented by a list of lengths Lengths 21 2 2N 7 1 and a list of densities Densities p1 p2 PN 7 2 where the baseline is given by N i 1 In C lists are represented as pointers to the first element double lengths double densities Many of the GLoBES baseline functions take and return such lists as parameters and are therefore more sophisticated to handle In general any function returning lists allocates the memory for them It is then up to the user to free this memory In addition they n
22. as in the file It is also possible to switch off one detector effect after the other First one can switch off the post smearing efficiencies f and the post smearing backgrounds g Next one can switch off the energy resolution function with b and view the rates before smearing If the s option is also used the number of lines in the output will be given by sampling_points Another effect of the b option is that the post smearing efficiencies and backgrounds are no longer taken into account Therefore the g and f options now apply to the pre smearing efficiencies and the pre smearing backgrounds Thus globes c b g f FILE produces the raw event rate corresponding to the convolution of flux probability and cross section which is neglecting all detector effects Rule level The next logical step after checking the channel rates is to investigate the rule rates The rule rates are returned with the option r This option takes as an optional argument the rule number starting at zero If no argument is given all rules will be displayed By default the sum of the event rates in each rule is shown as well as for each component within the rule Each rule is preceeded by a line with the same rule name as in the file It is also possible for rules to switch off one detector effect after the other with the limitation that rules only make sense after the energy resolution function has been applied to each channel Therefore
23. auxiliary parameters of the rule The total x for the considered experiment is finally obtained by repeating this procedure for all rules and adding their x values In general the situation is more complicated because of the usage of many systematical errors More details about systematics parameters and the definition of signal background and oscillation channels can be found in Sec 9 6 too The systematics minimization of an experiment can be easily switched on and off with glbSwitchSystematics i e one can also compute the x with statistics only In addition several options for systematics are available such as only using total event rates without spectral information For details we refer to Chapter 7 26 CHAPTER 3 Calculating x with systematics only 27 Chapter 4 Calculating x projections how one can include correlations This chapter deals with the rather complicated issue of n parameter correlations It is one of the greatest strengths of this software to include the full n parameter correlation in the high dimensional parameter space with reasonable effort Of course calculating x projections is somewhat more complicated than using systematics only Therefore we use a simple step by step introduction to the problem 4 1 Introduction In principle the precision of an individual parameter measurement including correlations in the y approach can be obtained as the projection of the n dimensional fit manifold ont
24. corresponding nuisance parameter We further on also refer to the mean as the central value and to the standard deviation as the error The latter corresponds to the actual systematical uncertainty The resulting x is then minimized with respect to all nuisance parameters which leads to 2 Xpull k Xpun A min va C Ea A 9 24 i Here A refers to the oscillation parameters including the matter density p One advantage of the pull method is that whenever the number N of data points is much larger than k it is numerically easier to compute X2 than to invert the N x N covariance matrix For the experiments considered here N is typically 20 and k 4 which means that the pull method is numerically much faster Moreover it is more flexible and allows the inclusion of systematical errors also for a Poissonian x function In Ref 12 it has been demonstrated that the pull method and the covariance based approach are equivalent for a Gau ian and linear model In general there is a separate Kun for each rule r i e pair of signal and background spectra with a separate set of nuisance parameters Thus Xul is the sum of all individual x3 s By the minimization the dependence on the k nuisance parameters has been eliminated from xZun Now we can introduce the different systematical errors The two most important and most easily parameterized systematical errors are the normalization and an energy calibra
25. for each type of quantity is used in order to avoid confusion about the definition of individual parameters Table 2 2 summarizes the units of the most important quantities In principle the event rates are proportional to the product of source power x target mass x running time which we call integrated luminosity Since especially the definition of the source power depends on the experiment type the quantities of the three luminosity components are not unique and depend on the experiment definition Usually one uses detector masses in kilotons for beam experiments and detector masses in tons for reactor experiments Running times are normally given in years where it is often assumed that the experiment runs 100 of the year Thus for shorter running periods the running times need to be renormalized Source powers are usually useful parent particle decays per year neutrino factories 3 beams target power in mega watts superbeams or thermal reactor power in giga watts reactor experiments Since the pre defined experiments in Table 2 1 are given for specific luminosities it is useful to read out and change these parameters of the individual experiments Function 2 4 void glbSetSourcePower double power int exp int fluxno sets the source power of experiment number exp and flux number fluxno to power The defi nition of the source power depends on the experiment type as described above Function 2 5 double glbGetSourcePower int ex
26. function R E E has been already introduced in Sec 9 4 where a definition has been given in Eq 9 4 Instead of using Eq 9 4 directly we apply a slightly different definition of the post smearing efficiencies e E In general e E has to be determined by means of a Monte Carlo simulation of the experiment This usually involves a binning of the simulated events in the reconstructed energy E Therefore one simplify Eq 9 6 by E AE 2 E AE 2 dE R E E amp E amp dE R E E 9 7 E AE 2 E AE 2 Here the are the binned post smearing efficiencies which will be set within the corre sponding channel environment see below From Eq 9 6 it is obvious that the integra tion with respect to the reconstructed energy E can be performed independently of the oscillation parameters We define the bin kernel Kf for the ith bin as E AE 2 KS E 1 dE R E E 9 8 Ei AE 2 With this definition Eq 9 6 can be re written as oo no N L amp f dE E P E o E K E 9 9 nm 0 f E There is no principle reason why one should not evaluate this integral directly by the usual numerical methods However it turns out that this is very slow in many cases 9 5 Energy resolution function 75 Sampling point level Integral evaluation sampling_min Ssampling_points Ssampling_max oo 0 0 0 0 0 9 0 9 9 9 0 00 eC eCe 9 Incident
27. glbSetRates Iteration over all values to be computed double x y res for x 4 0 x lt 2 0 0 01 x x 2 0 50 for y 0 0 y lt 200 0 0 01 y y 200 0 50 Set parameters in vector of test values glbSetOscParams test_values asin sqrt pow 10 x 2 GLB_THETA_13 glbSetOscParams test_values y M_PI 180 0 GLB_DELTA_CP Compute Chi2 for all loaded experiments and all rules res glbChiSys test_values GLB_ALL GLB_ALL AddToOutput x y res The resulting data can then be plotted as a contour plot 2 d o f 200 cp Degrees 10 sin 2013 CHAPTER 3 Calculating x with systematics only 25 One example for a systematics parameter the signal normalization error i e an error to the overall normalization of the signal For illustration we assume that the signal event rate in the ith bin s of one oscillation channel is altered by the overall normalization auxiliary parameter of this channel i e Si s ns S 1 ns 3 1 where n is the signal normalization parameter The total number of events in the ith bin x also includes the background event rates b i e amp si b which may have their own systematics parameters In order to implement an overall signal normalization error On the x which includes all event rates x of all bins is minimized over the auxiliary parameter ns 2 v min tn J ua 3 2 This minimization is done independently for all
28. intended mainly for the package s developers If you use it you may have to get all sorts of other programs in order to regenerate files that came with the distribution 5 Since you ve installed a library don t forget to run ldconfig Installation without root privilege Install GLoBES to a directory of your choice GLB_DIR This is done by configure prefix GLB_DIR and then follow the usual installation guide The only remaining problem is that you have to tell the compiler where to find the header files and the linker where to find the library Furthermore you have to make sure that the shared object files are found during execution Running configure also produces a Makefile in the examples subdirectory which can serve as a template for the compilation and linking process since all necessary flags are correctly filled in Another solution is to set the environment variable LD_RUN_PATH during linking to GLB_DIR lib Best thing is to add this to your shell dot file e g bashrc Then you can use A typical compiler command like gcc c my_program c IGLB_DIR include and a typical linker command like 96 CHAPTER GLoBES installation g my_program o lglobes LGLB_DIR lib o my_executable More information on this issue can be obtained by having a look into the mentioned Makefile in examples CAVEAT It is in principle possible to have many installations on one machine Especially the situation of having an installation
29. it is not possible to use b together with r or to switch off any pre smearing efficiencies or backgrounds One can however switch off the post smearing efficiencies f and the post smearing backgrounds g for each channel Since the definition of a rule also contains so called coefficients it is possible to switch them off with i This options also deactivates any setting of backgroundcenter Output The default output stream is stdout The output can be re directed to a file using the o option which takes as mandatory argument the file name The default output format aims at maximal readability for a human eye In many cases however the output of globes is produced as input for other programs There are some features to adjust the output format Usually one would like to omit the channel and rule names by using simple printing S instead of pretty printing P There are special options for certain special formats m produces Mathematica list output which can be directly visualized by MultipleListPlot The option u uses the same principal formatting as m but it allows to specify the left middle and right delimiters in constructing the list such as 2Mathematica is a trademark of Wolfram Inc 90 CHAPTER 10 Testing amp debugging of AEDL files left left 1 middle 2 middle 3 right middle left left 1 middle 2 middle 3 right right This is with left middle and right equivalent to t
30. location if any given in the Document for public access to a Transparent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission K For any section Entitled Acknowledgements or Dedications Preserve the Title of the section and preserve in the section all the substance and tone of each of the contributor acknowledgements and or dedications given therein L Preserve all the Invariant Sections of the Document unaltered in their text and in their titles Section numbers or the equivalent are not considered part of the section titles M Delete any section Entitled Endorsements Such a section may not be included in the Modified Version N Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section O Preserve any Warranty Disclaimers If the Modified Version includes new front matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These
31. matrix entries in K for the ith energy bin is defined to run from column kj lower index to column kf upper index An example for a smearing matrix is Qoo Qoi Ao2 403 Qio Qil A 2 Q13 Aa Q21 Q22 Q23 Q24 Q25 Kij 432 433 G34 435 436 bins rows 9 20 Q43 Q44 G45 Q46 Q47 i i ki ki N oa sampling_ points columns 9 6 Rules and the treatment of systematics 81 where the unshown entries are zero Thus the values of K have to be specified between kj and kj in the form kj ki Kini Kinigas 5 Kir energy name lt energy 0 2 0 8634265 0 0682827 4e 06 0 4 0 1507103 0 6965592 0 1507103 0 00101 1e 07 gt Note that the sum of all entries in each column should be equal to unity since all of the incoming neutrinos should be assigned to energy bins In many practical cases however the definition of the energy smearing can lead to sums smaller than unity such as in the case of truncated Gau ian distributions The sum of entries in each row is not defined since the events might be unevently distributed into the energy bins according to the energy resolution function 9 6 Rules and the treatment of systematics The set of rules for an experiment is the final link between the event rate computation and the statistical analysis The information in the rules specifies how the x is computed based upon the raw event rates given by the channels and possible systematical errors Therefore a
32. neutrino energy Pre smearing efficiencies smearing matrix approx energy res approx calibr error Reconstructed SI energy Segmax Bin level Defined by experiment Analysis level Energy cut Brenn energy energy_window Figure 9 1 The different evaluation levels for the energy smearing in GLoBES Therefore we will introduce two different approximation schemes for different applications in the next two subsections In either case the integrand in Eq 9 9 has to be evaluated at fixed sampling points These sampling points have to directly or indirectly be defined by the user Before we come to the calculation algorithms it is useful to understand the general evaluation algorithm As it is illustrated in Fig 9 1 GLoBES uses several levels with respect to the energy ranges Sampling point level This level is used internally to evaluate the integrand in Eq 9 9 at all sampling points The energy scale is the actual incident neutrino energy E For a manual definition of the sampling points use sampling_points 20 sampling_min 4 0 sampling_max 50 0 for equidistant sampling points If no values are given for these vari ables they are assumed to be equal to their corresponding counter part at bin level i e sampling_points bins sampling_min emin and sampling max emax Arbitrarily spaced sampling points can be specified with sampling_stepsize
33. of the incident neutrino which can not be directly observed translates via secondary particles and the detection properties into a distribution of possible energy values This process is illustrated in Fig 8 1 for the energy variable The same in principle applies to the nature Detector True Energy Reconstructed Energy Figure 8 1 A detector maps a true parameter value onto a distribution of reconstructed parameter values This is illustrated here for there energy of the neutrino flavor However in this case only discrete values are applicable Note that the reconstructed neutrino energy and the neutrino flavor are the only observables in GLoBES This picture can also be formulated in a more mathematical way Let us define x as the true parameter value and x as the reconstructed parameter value Similarly f x is the distribution of true parameters values and p z is the distribution of reconstructed param eter values Then the detector function D x x which describes the mapping performed by the detector is given by pay fe f x D x x 8 1 Obviously Eq 8 1 only describes the detector properly if the linearity condition is ful filled Within this model a detector is completely specified by a set of D E E for the 8 1 General concept of the experiment simulation 59 PEHEEUELEEEENEEEERTELEH er tunnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn Figure 8 2 General concept of a channel en
34. rule has two parts The first part describes how signal and background events are composed out of the channels and the second part specifies which systematical errors are considered as well as their values For a rule the splitting in signal and background is useful for the treatment of systematics as we will se later Each rule will lead to a Ax value which means that all Ay s of the different rules will be added for the whole experiment Within each rule the event rates are added and the systematics is considered to be independent of the other rules Thus it is convenient to combine the above defined channels for different oscillation patterns and interaction types into one logical construction which is the rule For example a superbeam usually has two rules One for the v appearance rates and one for the v disappearance rates In each case contributions of several interaction types as well as from the v contamination of the beam will lead to a number of contributing signal and background event channels For each rule the signal event rate s in the ith bin can be composed out of one or more channels by Si Mey NG Aa NP 9 21 where the a s are overall normalization factors efficiencies determined by the properties of the detector Note that bin based energy dependent efficiencies can be defined with the post smearing efficiencies in the last section In addition note that in most cases it makes sense to have onl
35. rule to the value value The function returns 1 if not successful Function 7 11 int glbGetErrorDim int exp int rule int on_off returns the error dimension for systematics on on_off is GLB_ON or off on_off is GLB_OFF of experiment exp and rule rule Except from the general treatment of systematics one can read out and write the signal and background errors as well as the background centers For the definitions of these quantities see Sec 9 6 Function 7 12 int glbSetSignalErrors int exp int rule double norm double tilt sets the signal errors of experiment exp and rule rule to norm nor malization error and tilt tilt calibration error 7 2 Systematics 51 Example The impact of systematics correlations and degeneracies Here it is demonstrated how one can successively include systematics correlations and degeneracies at the example of the sin 20 3 sensitivity limit An important part of this example is how two switch the systematics off i e how to obtain the sensitivity limit from statistics only Since this example is very advanced we only show the respective function of the code Calculate chi2 with statistics only double CalcNoSystematics double theldm double thex Switch systematics off for all exps and all rules glbSwitchSystematics GLB_ALL GLB_ALL GLB_OFF Calculate Chi2 list as if systematics were on double res CalcSystematics theldm thex Switch systematics on for all e
36. systematics is treated independently from the other rules e For each rule the Ay is computed the Ay s from all rules are added Of course an abstract experiment definition language can not simulate all possible types of experiments As we have seen there are several assumptions for source and detec tor However it turns out that GLoBES can be applied to a large number of experiment types such as conventional beams superbeams neutrino factories G Beams and reactor experiments 8 2 A simple example for AEDL 61 Set ee i A nm Figure 8 4 General concept of an experiment 8 2 A simple example for AEDL Experiments are in GLoBES defined by the Abstract Experiment Definition Language AEDL The experiment definition is written into a text file using the AEDL syntax Currently a number of pre defined experiment definition files are provided with GLoBES which have to be modified manually in order to define new experiments The application software then uses this text file to initialize the experiment where other secondary files might read for source fluxes cross sections etc In this section we show the definition of a very simple neutrino factory in AEDL where we do not go into details In the next chapter we will discuss each of the individual steps in detail The first line of every experiment definition file has to be GLOBES in order not to confuse it with some other file format First we instruct GLoBES to
37. the external input with 10 external precisions for the solar parameters and 5 matter density uncertainties for all experiments looks like this glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues true_values glbSetInputErrors input_errors 4In fact accelerator based long baseline experiments are primarily sensitive to the product sin 2613 Am3 which means that these errors effectively add up to an error of this product of about 15 4 3 Projection onto the sin 20 3 axis or dcp axis 31 In this example the starting values are set to the true simulated values Remember that initially the matter density scaling factors are all 1 0 which means that they do not need to be adjusted for the starting values Though the priors are an elegant way to treat external input there are also some complications with priors The following hints are for the more advanced GLoBES user 1 The priors are only added once to the final x no matter how many experiments there are simulated This is already one reason besides the minimization why the sum of all projected x s of the individual experiments cannot correspond to the x of the combination of all experiments 2 Priors are not used for parameters which are not minimized over i e kept fixed This will be important together with arbitrary projections using glbChiNP A more subtile consequence is the compar
38. the wide range of software distributed through that system in reliance on consistent application of that system it is up to the author donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License If the distribution and or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries so that distribution is permitted only in or among countries not thus excluded In such case this License incorporates the limitation as if written in the body of this License The Free Software Foundation may publish revised and or new versions of the General Public License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns Each version is given a distinguishing version number If the Program specifies a version number of this License which applies to it and any later version you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation If the Program does not specify a version number of this License you m
39. titles must be distinct from any other section titles You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard You may add a passage of up to five words as a Front Cover Text and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Modified Version Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover text for the same cover previously added by you or by arrangement made by the same entity you are acting on behalf of you may not add another but you may replace the old one on explicit permission from the previous publisher that added the old one The author s and publisher s of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version 5 COMBINING DOCUMENTS You may combine the Document with other documents released under this License under the terms defined in section 4 above for modified versions provided that you include in the combination all of the Invariant Sections of all of the original documents unmodified and list them all as Invariant Sections of your combined work in i
40. to GLB_W_BG or GLB_WO_BG Note that the post smearing efficiencies and backgrounds cannot be taken into account if the rates are returned before the energy smearing The return value is 0 if successful and 1 if unsuccessful Function 6 13 int glbGetChannelRates double data size_t length int exp int channel int smearing writes the binned raw channel rates to the list data and the length of this list to length A specific experiment exp and a specific channel channel have to be chosen The function may return the rates before smearing is GLB_PRE or after smearing is GLB_POST the energy smearing where no user defined data pre post smearing efficiencies or backgrounds are taken into account The return value is 1 if unsuccessful Function 6 14 int glbGetUserData double data size_t length int exp int channel int smearing int bgeff writes the binned user defined backgrounds or efficiencies to the list data and the length of this list to length A specific experiment exp and a specific channel channel have to be chosen The function may return the pre smearing is GLB_PRE or post smearing is GLB_POST smearing backgrounds bgeff is GLB_BG or efficiencies bgeff is GLB_EFF The return value is 1 if unsuccessful Since GLoBES reserves the memory for the lists returned in these functions which it al locates on an internal stack one has to reset the stack at the end of the rates access with 46 CHAPTER 6 Obtainin
41. to the ones in the last section They can for example be used to obtain a figure similar to Fig 4 1 left The example on page 32 illustrates then the difference between the projections of the eggs within the sin 20 3 dcp plane onto the 3 axis Though the running time for one call of these functions is somewhat shorter than the one for the sin 2843 or dcp projections one has to compute a two dimensional array for such a figure instead of a one dimensional list Therefore the overall computational effort is much higher i e in the order of hours In many cases it is therefore convenient to run glbChiSys first to obtain a picture of the manifold and to adjust the parameter ranges Then one can run glbChiThetaDelta for a complete evaluation of the problem including correlations In principle one can also use three or more dimensional projections In addition one may want to use a different set of parameters for single or two parameter projections The very flexible function glbChiNP is designed for this purpose However because of its flexibility it involves more sophistication In order to define arbitrary projections we introduce the vector glb_projection which is very similar to the oscillation parameter vector glb_params Normally the user does not need to access this type directly A set of function similar to the ones for glb_params is provided The purpose of glb_projection is to tell GLoBES what parameters are fixed a
42. user defined variable one has to assign it with glbDefineAEDLVariable before the experiment is initialized with glbInitExperiment Function 7 18 void glbDefineAEDLVariable const char name double value assigns the value value to the AEDL variable name 7 4 Algorithm parameters Filter functions 53 In our energy resolution example one could now loop over the energy resolution such as with int i for i 5 1 lt 20 i glbClearExperimentList glbDefineAEDLVariable myres 0 01 i glbInitExperiment do something Note that one does not have do re initialize the oscillation parameter vectors every time within the loop as long as the number of experiments does not change In order to clear the external variable stack if one is excessively using it one can use Function 7 19 void glbClearAEDLVariables clears the AEDL variable list This function is called automatically upon exit of the program 7 4 Algorithm parameters Filter functions The oscillation frequency filters to filter fast oscillations can also be accessed by the user interface For details of the filter functions we refer to Sec 9 5 of the AEDL manual In particular there are a number of functions Function 7 20 int glbSetFilterState int on_off sets the currently used filter state to on GLB_ON or off GLB_OFF Function 7 21 int glbGetFilterState returns the currently used filter state Function 7 22 int glbSetFilterStateInExperimen
43. 3 densitytab 3 5 lengthtab 3000 0 The possible options for matter density profiles are summarized in Table 9 1 9 3 Cross sections Cross sections will later be used as part of the channel definition see Sec 9 4 Similar to the source fluxes they are provided by the user as a data file cross name lt cross_file user_file_i dat 9 4 Oscillation channels 71 This cross section can later be refered to by name Cross sections are in GLoBES given as differential cross section per energy gt E 0 B B 10 8 9 2 03 o GeV The software assumes that the cross section files are text files with seven columns and 1001 lines of the form logo E Gy Gy v Here the logarithms of the energy values have to be equidistant For arbitrary energies linear interpolation is used If the energy leaves the range of values given in the file 0 0 will be assumed In general it is advisable to provide the cross sections in the range between sampling_min and sampling_max cf Sec 9 5 Unused cross sections have to be filled with zeros and can not be just omitted Like the flux files the cross section files accept one line comments which start with and end with the linefeed character n they are not counted as a line and their content is discarded This comments are useful to provide meta information about the cross sections like units or the origin of the information This is also the default method to poi
44. 88 errors 88 oscillation parameters 87 output 89 rule rates 89 spectral rates 88 total rates 88 variable substitution 90 INDEX verbosity 88 warnings 88 GLoBES tour 3 Initialization 13 GLoBES library 13 experiments 16 libglobes 13 Installation 13 93 97 prerequisites 93 w o root privilege 95 Integrated luminosity 18 libglobes 13 87 Low level information 43 Mass hierarchy 19 40 Matter density scaling factor 23 change profile 47 of the earth 69 profile 19 scaling factor 19 29 34 uncertainty 23 Minimization all parameter 39 Minimizer 27 31 iterations 21 priors 31 Oscillation parameter vectors 19 probabilities 43 switching off 73 Parameter vector handling 21 Path resolution 17 PREM see Matter density Program 14 Projection 013 cp plane 35 definition 36 axis 31 hyperplane 35 119 of manifold 27 32 type 36 Pull method 23 Reference rate vector 21 Referencing cross section data 71 data in GLoBES III flux data 69 matter profile data 70 Rule 59 81 Running time 18 Set oscillation parameters 21 Signal errors 50 Simulated data 21 Smear matrix 72 Source power 18 Standard functions table 4 Systematics 23 50 23 on off 50 51 True values 21 Units in GLoBES table 17 Version control 22 85
45. BES i e about oscillation probabilities rates and other information lower than on the x level 6 1 Oscillation probabilities GLoBES can compute the probabilities in vacuum with the following function Function 6 1 double glbVacuumProbability int 1 int m int panti double E double L returns the neutrino oscillation probability vy Vm for the energy E and the baseline L in vacuum The parameter panti is 1 for neutrinos and 1 for antineutrinos In addition the oscillation probabilities in matter can be obtained with Function 6 2 double glbProfileProbability int exp int 1 int m int panti double E returns the neutrino oscillation probability vy Vm for the en ergy E in matter where the matter density profile is the one of experiment exp The parameter panti is 1 for neutrinos and 1 for antineutrinos The matter density profile including baseline is the one from the last evaluated experiment 6 2 AEDL names Since in AEDL rules cross section fluxes etc carry a name by which they can be refered to and in C they cary only an integer as index it is sometimes difficult to figure out the correct correspondence Therefore the information about this correspondence obtained during parsing is stored and can be accessed within C by these two functions Function 6 3 int glbNameToValue int exp const char context const char name Converts an AEDL name given as argument name into the corresponding C index The variabl
46. Chapter 2 Note that all functions but glbChiSys are using minimizers which have to be initialized with glbSetInputErrors and glbSetStartingValues first CHAPTER 1 A GLoBES tour 5 Assign values to our standard oscillation parameters glbDefineParams true_values theta12 thetal3 theta23 deltacp sdm 1dm Compute the simulated data with our standard parameters glbSetOscillationParameters true_values glbSetRates Return the oscillation probabilities in vacuum and matter for the electron neutrino as initial flavor int i fprintf stream nOscillation probabilities in vacuum for i 1 i lt 4 i fprintf stream 1 gt i g i glbVacuumProbability 1 i 1 50 3000 fprintf stream nOscillation probabilities in matter for i 1 i lt 4 i fprintf stream 1 gt i Ag i glbProfileProbability 0 1 1 1 50 Output Oscillation probabilities in vacuum 1 gt 1 0 999953 1 gt 2 2 69441e 05 1 gt 3 1 98019e 05 Oscillation probabilities in matter 1 gt 1 0 999965 1 gt 2 2 02573e 05 1 gt 3 1 49021e 05 Now assign fit values where we will test the fit value sin 2043 0 0015 glbCopyParams true_values fit_values glbSetOscParams fit_values asin sqrt 0 0015 2 GLB_THETA_13 Compute x with systematics only for all experiments and rules chi2 glbChiSys fit_values GLB_ALL GLB_ALL fprintf stream chi2 with systematics only g n n chi2 Output chi2 with systematics only 22 3984
47. GLoBES General Long Baseline Experiment Simulator User s and experiment definition manual Patrick Huber Manfred Lindner Walter Winter Version from August 3 2004 for GLoBES 2 0 D C Institut f r Theoretische Physik Physik Department Technische Universit t M nchen James Franck Strasse D 85748 Garching Germany Copyright 2004 The GLoBES Team Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documenta tion License Version 1 2 or any later version published by the Free Software Foundation with the invariant Sections Terms of usage of GLoBES and Ac knowledgments no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation Li cense What is GLoBES GLoBES General Long Baseline Experiment Simulator is a flexible software package to simulate neutrino oscillation long baseline and reactor experiments On the one hand it contains a comprehensive abstract experiment definition language AEDL which allows to describe most classes of long baseline experiments at an abstract level On the other hand it provides a C library to process the experiment information in order to obtain oscillation probabilities rate vectors and Ay values Currently GLoBES is available for GNU Linux Since the source code is included the port to other operating systems is in principle possible
48. PACK Linear Algebra PACKage www netlib org lapack f2c Fortran to C www netlib org f2c GSL The GNU Scientific Library www gnu org software gsl The library libglobes should in principle compile with any ANSI C C compiler but the globes binary uses the argp facility of glibc to parse its command line options All those libraries are also available as rpm s from the various distributors of GNU Linux See their web sites for downloads Due to the rather difficult nature of the build process of BLAS and LAPACK it is recommended that one uses a suitable rpm instead In addition there is a good chance that gcc f2c and GSL are already part of your installation Furthmore you need a working make to build and install GLoBES In future releases it is planned to at least make LAPACK obsolete because then also BLAS and f2c would drop out Furthemore there is no priniciple reason why one should not get rid of any C parts This will greatly simplify the build process and reduce the requirements for installation 94 CHAPTER GLoBES installation Installation Instructions GLoBES follows the standard GNU installation procedure To compile GLoBES you will need gcc After unpacking the distribution the Makefiles can be prepared using the con figure command configure You can then build the library by typing make A shared version of the library will be compiled by default The library can be installed using the command make ins
49. StartingValues true_values glbSetInputErrors input_errors Define my own two parameter projection for glbChiNP Only deltacp is free x glbDefineProjection th13_projection GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FIXED GLB_FIXED glbSetProjection th13_projection Iteration over all values to be computed double x resi res2 for x 4 x lt 2 0 0 001 x x 2 0 50 Set fit value of stheta glbSetOscParans test_values asin sqrt pow 10 x 2 1 Guess fit value for deltacp in order to safely find minimum glbSetOscParams test_values 200 0 2 x 4 M_PI 180 3 Compute Chi2 for user defined two parameter correlation resi glbChiNP test_values NULL GLB_ALL Compute Chi2 for full correlation minimize over all but theta13 res2 glbChiTheta test_values NULL GLB_ALL AddToOutput x res1 res2 The two lists of data then represent the sin 2843 precisions with two parameter corre lations gray shaded and multi parameter correlations arrows 0 u 1074 107 107 sin 2013 Same parameters as on page 24 and in Fig 4 1 but 1 d o f 4 3 Projection onto the sin 20 3 axis or dcp axis 33 Correlation between sin 26 3 and dcp Projection onto sin 2013 axis 200 lo 7 t t 4 4 4 20 7 Ltt 3a 150 Ly on LAAT amp 100 LH ne ICT S YKI 7 50 gl 0 107 10 10 107 107 107 sin 2613 sin 2613 Figure
50. TS found in Part I within the boxed pages As complete files they are also available in the GLoBES software package The GLoBES software may have two target groups Physicists who are mainly inter ested in optimizing the potential of specific experimental setups and others who are mainly interested in the physics potential of different experiment types from a theoretical point of view For the first group AEDL could be the most interesting aspect of GLoBES where the user interface is only a tool to obtain specific parameter sensitivities In this case GLoBES could serve as a unified tool for the comparison and optimization of different experiment setups on equal footing where it is the primary objective to simulate the experiments as accurate as possible In addition changes in experimental parameters such as efficiencies or the energy resolutions can quickly be tested For the second user group the pre defined experiment definition files might already be sufficient to test new conceptual approaches and the user interface is the most interesting aspect for sophisticated applications includ ing correlations degeneracies and multi experiment setups In either case the GLoBES software could serve as a platform for the exchange of experiment definitions and for an efficient splitting of work between experimentalists and theorists The user interface functions are described in Part I of this manual which is the user s manual In t
51. The software as well as up to date versions of this manual can be found at this URL http www ph tum de globes GLoBES allows to simulate experiments with stationary neutrino point sources where each experiment is assumed to have only one neutrino source Such experiments are neu trino beam experiments and reactor experiments Geometrical effects of a source distri bution such as in the sun or the atmosphere can not be described In addition sources with a physically significant time dependencies can not be studied such as supernove It is however possible to simulate beams with bunch structure since the time dependence of the neutrino source is physically only important to suppress backgrounds On the experiment definition side either built in neutrino fluxes e g neutrino factory or arbitrary fluxes can be used Similarly arbitrary cross sections energy dependent effi ciencies the energy resolution function the considered oscillation channels backgrounds and many other features can be specified For the systematics energy normalization and calibration errors can be simulated Note that the energy ranges and windows as well as the bin widths can be almost arbitrarily chosen which means that variable bin widths are allowed Together with GLoBES comes a number of pre defined experiments in order to demonstrate the capabilities of GLoBES and to provide prototypes for new experiments With the C library one can extract the Ay fo
52. These constants can not only be defined within one AEDL file but also by the calling C program which allows to use a simple but powerful variable substitution mechanism as described in Sec 7 3 In addition some simple algebraic manipulations are possible such as 66 CHAPTER 8 Getting started Pitti Pi72 sin Pi 2 The following mathematical functions from lt math h gt are available sin cos tan asin acos atan log log10 exp sqrt These functions can be used everywhere where otherwise only a scalar number would appear However they can not be applied to lists such as sin 1 2 3 will not work Finally note that a line feed character n is necessary at the end of the input alter natively you can put a comment at the end 67 Chapter 9 Experiment definition with AEDL In this chapter we give a detailed definition of the AEDL features We also show the underlying mathematical concepts where applicable We do not exactly follow the separa tion of source oscillation and detection properties since most issues more or less involve the detection Instead we illustrate many of the features of the GLoBES simulation suc cessively in the logical order of their definition and demonstrate how they translate into AEDL 9 1 Source properties and integrated luminosity As we have disussed before GLoBES can only deal with point sources Thus it is not possible to study effects from the finite size of the neutrino produc
53. alues glbSetOscParams fit_values asin sqrt 0 0015 2 GLB_THETA_13 Here comes the x with systematics only for all experiments and rules chi2 glbChiSys fit_values GLB_ALL GLB_ALL fprintf stream chi2 with systematics for all exps Ag n chi2 Output chi2 with systematics for all exps 31 0797 Compute x for each experiment and compute the sum chi2 glbChiSys fit_values 0 GLB_ALL fprintf stream chi2 with systematics for 3000km g n chi2 chi2b glbChiSys fit_values 1 GLB_ALL fprintf stream chi2 with systematics for 7500km g n chi2b fprintf stream The two add again to 7g n n chi2 chi2b Output chi2 with systematics for 3000km 22 3984 chi2 with systematics for 7500km 8 68131 The two add again to 31 0797 10 CHAPTER 1 A GLoBES tour Similarly compute the x with correlations for each experiment and their combination Compare it to the x for all experiments the sum of the individual results is not equal to the x of the combination anymore Note that there are now two densities in the output vectors glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues true_values glbSetInputErrors input_errors chi2 glbChiTheta fit_values minimum 0 fprintf stream chi2 with correlations for 3000km g n chi2 glbPrintParams stream minimum chi2b glbChiTheta fit_values minimum 1 fprintf stream nchi2 w
54. ams Each of these scaling factors has 1 0 as pre defined value Since it is in most cases not necessary to change this value the user does not need to take care of it For a constant matter density it is simply the ratio of the matter density and the average matter density specified in the experiment definition i e i pi p For a matter density profile it acts as an overall normalization factor The matter density in each layer is multiplied by this factor In most cases one wants to take a scaling factor of 1 0 here which simply means taking the matter density profile as it is given in the experiment definition For the treatment of correlations however an external precision of the scaling factor might be used to include the correlations with the matter density uncertainty Note that the glb_params structures must not be initialized before all experiments are loaded since the number of matter densities can only be determined after the experiments are initialized Similarly any change in the number of experiments requires that the parameter structures be re initialized 7 e freed and allocated again Note Inverting the mass hierarchy is not precisely the same than to change from Am Am3 In this case the absolute value of Am2 changes also which introduces a new frequency to the problem Therefore if we assume normal hierarchy whenever Am3 gt 0 the corresponding point in parameters space for inverted hierarchy is given by A
55. and tons for a reactor experiment In any case it is a good idea to document the choices made by the user by corresponding comments in AEDL The quantity which can be used to scale the overall integrated luminosity of an exper iment is the fiducial detector mass For example target_mass 50 0 defines a 50 kt detector for a neutrino factory There are two principal ways to initialize a neutrino flux Either one can use a built in source or one can provide a file In both cases a flux is defined by the environment flux such as flux name lt time 8 0 gt with a running time of 8 years Note that the running time is used within the flux envi ronment This feature can be used to load the neutrino and antineutrino fluxes separately in order to combine them with different running times within one experiment The name of the flux name will later be refered to in the channel definitions For a built in neutrino source one has to specify which built in spectrum has to be used as well as its parameters The software will then automatically calculate the neutrino spectrum Note that in this case there is no degree of freedom in the choice of the source units Currently two built in fluxes are available u decay builtin 1 and u decay builtin 2 In these cases the muon energy enery of the parent particle has to be specified together with the number of useful decays per year Thus an example to set up a neutrino fact
56. arameters have to be set by the function glbSetOscillationParameters and the reference rate vector i e the data has to be computed by a call to glbSetRates This has to be done before any evaluation function is used and after the experiments have been initialized and also the experiment parameters have been adjusted which could change the rates such as baseline or target mass This means that after any change of an experiment parameter glbSetRates has to be called Matter effects are automatically included as specified in the experiment definition We have the following functions to assign and read out the vacuum oscillation parameters 22 CHAPTER 2 GLoBES basics Function 2 21 int glbSetOscillationParameters const glb_params in sets the vacuum oscillation parameters to the ones in the vector in Function 2 22 int glbGetOscillationParameters glb_params out returns the vac uum oscillation parameters in the vector out The result of the function is 0 if the call was successful The reference rate vector is then computed with Function 2 23 void glbSetRates computes the reference rate vector for the neutrino oscillation parameters set by glbSetOscillationParameters A complete example for a minimal GLoBES program can be found on Page 14 2 5 Version control In order to keep track of the used version of GLoBES the software provides a number of functions to check the GLoBES and experiment versions It is up to the user to implement
57. arity and competitiveness by equal means within one program In general many GLoBES functions take the experiment number as a parameter which runs from 0 to glb_num_of_exps 1 in the order of their initialization in the program In addition using the parameter value GLB_ALL as experiment number initiates a combined analysis of all loaded experiments In general GLB_ALL can be used in many cases where there is an argument selecting i out of N e g the 1st experiment out of 5 or the 5th rule of 20 In those cases using GLB_ALL is equivalent to calling the corresponding function for all i in N and add the effect of each invocation like in for i 0 i lt N i result some_function i is the same as result some_function GLB_ALL Here the meaning of add is that whatever the desired result of calling some_function is this result is obtained for each iin N e g setting the baseline in all experiments to a certain value or or compute the x for each experiment and return the total result There are however some functions where the action performed or the result is so complex that is not possible or sensible to perform this for all in N Calling these functions with GLB_ALL as argument will in any case result in an exit status indicating failure and the function will produce an error message For storing the experiments GLoBES uses the initially empty list of experiments glb_experiment_list To add a pre defined exper
58. ay charge a fee for the physical act of transferring a copy and you may at your option offer warranty protection in exchange for a fee You may modify your copy or copies of the Program or any portion of it thus forming a work based on the Program and copy and distribute such modifications or work under the terms of Section 1 above provided that you also meet all of these conditions a You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change b You must cause any work that you distribute or publish that in whole or in part contains or is derived from the Program or any part thereof to be licensed as a whole at no charge to all third parties under the terms of this License c If the modified program normally reads commands interactively when run you must cause it when started running for such interactive use in the most ordinary way to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty or else saying that you provide a warranty and that users may redistribute the program under these conditions and telling the user how to view a copy of this License Exception if the Program itself is interactive but does not normally print such an announcement your work based on the Program is not required to print an announcement These requirements apply to the modified work as a whole If identifiable sections
59. ay choose any version ever published by the Free Software Foundation If you wish to incorporate parts of the Program into other free programs whose distribution con ditions are different write to the author to ask for permission For software which is copyrighted by the Free Software Foundation write to the Free Software Foundation we sometimes make ex ceptions for this Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally No WARRANTY BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE THERE IS NO WARRANTY FOR THE PROGRAM TO THE EXTENT PERMITTED BY APPLICABLE LAW EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND EITHER EXPRESSED OR IMPLIED INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU SHOULD THE PROGRAM PROVE DEFECTIVE YOU ASSUME THE COST OF ALL NECESSARY SERVICING REPAIR OR CORRECTION IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER OR ANY OTHER PARTY WHO MAY MODIFY AND OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE BE LIABLE TO YOU FOR DAMAGES INCLUDING ANY GENERAL SPECIAL INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR
60. b Accompany it with a written offer valid for at least three years to give any third party for a charge no more than your cost of physically performing source distribution a complete machine readable copy of the corresponding source code to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or c Accompany it with the information you received as to the offer to distribute corresponding source code This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer in accord with Subsection b above The source code for a work means the preferred form of the work for making modifications to it For an executable work complete source code means all the source code for all modules it contains plus any associated interface definition files plus the scripts used to control compilation and installation of the executable However as a special exception the source code distributed need not include anything that is normally distributed in either source or binary form with the major components compiler kernel and so on of the operating system on which the executable runs unless that component itself accompanies the executable If distribution of executable or object code is made by offering access to copy from a designated place then offering equivalent access to copy the source code from the sam
61. by root and by a user at the same time might occur However it is strictly warned against this possibility since it is extremely likely to create some versioning problem at some time Advanced topics Compilers and Options Some systems require unusual options for compilation or linking that the configure script does not know about You can give configure initial values for variables by setting them in the environment Using a Bourne compatible shell you can do that on the command line like this CC c89 CFLAGS 02 LIBS lposix configure Or on systems that have the env program you can do it like this env CPPFLAGS I usr local include LDFLAGS s configure Compiling For Multiple Architectures You can compile the package for more than one kind of computer at the same time by placing the object files for each architecture in their own directory To do this you must use a version of make that supports the VPATH variable such as GNU make cd to the directory where you want the object files and executables to go and run the configure script configure automatically checks for the source code in the directory that configure is in and in If you have to use a make that does not supports the VPATH variable you have to compile the package for one architecture at a time in the source code directory After you have installed the package for one architecture use make distclean before reconfiguring for another architec
62. cientific journal It will evolve during time since it is intended for regular revision Besides that many ofthe data which are used by GLoBES and distributed together with it should be properly referenced For details see below Apart from that GLoBES is free software and open source t e it is licensed under the GNU Public License Referencing the data in GLoBES GLoBES wouldn t be useful without having high quality input data Much of these input data have been published elsewhere and the authors of those publications would appreciate to be cited whenever their work is used It is solely the user s responsibility to make sure that he understands where the input material for GLoBES comes from and if additional work has to be cited in addition to the GLoBES paper 1 To assist with this task we provide the necessary information for the data coming along together with GLoBES When using the built in Earth matter density profile the original source is Ref 2 All files ending with dat or glb in the data subdirectory of the GLoBES tar ball have on top a comment field which clearly indicates which works should be cited when using a certain file Make sure that dependencies are correctly tracked i e in some cases files included by other files need to be checked too for example cross section or flux files One can use the v3 option to globes to see which files are included It is recommended that you use the same style for your own i
63. conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies 3 COPYING IN QUANTITY CHAPTER GNU Free Documentation License 107 If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Document s license notice requires Cover Texts you must enclose the copies in covers that carry clearly and legibly all these Cover Texts Front Cover Texts on the front cover and Back Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the covers in addition Copying with changes limited to the covers as long as they preserve the title of the Document and satisfy these conditions can be treated as verbatim copying in other respects If the required texts for either cover are too voluminous to fit legibly you should put the first ones listed as many as fit reasonably on the actual cover and continue the rest onto adjacent pages If you publish or distribute Opaque copies of the Document numbering more than 100 you must either include a machine readable Transparent copy along with each Opaque copy or state in or with each Opaque copy a computer network location from which the general network using public has access
64. d in out where the fixed parameters are still at their input values If out is set to NULL this information will not be returned As an example the projection sequence for a minimization over dcp only looks like this glb_projection th13_projection glbAllocProjection glbDefineProjection th13_projection GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FIXED GLB_FIXED glbSetProjection th13_projection res1 glbChiNP test_values NULL GLB_ALL glbFreeProjection th13_projection In this case only the correlation with cp is taken into account Note that in the example on page 32 this projection is compared with the result including the full multi parameter correlation 38 CHAPTER 4 Calculating y projections how one can include correlations 39 Chapter 5 Locating degenerate solutions In the last chapter we introduced the projection of any set of k parameters onto any n k dimensional hyperplane which was performed by the minimization over the k free fit parameters Similarly one can minimize over all n parameters to find the local minimum close to any starting point This approach is very useful for the exact numerical location of a degeneracy if its approximate position is known For the determination of the approximate position one can use analytical approaches or an educated guess Though the usage of the all parameter minimizers is quite simple one should keep in mind that they are local minimizers Therefore one may need
65. de by about three times the energy calibration error 84 CHAPTER 9 Experiment definition with AEDL Eventually the total event rate x in a bin t is given by xi a b c d sila b b c d 9 28 and is thus a function of four parameters The four parameters a b c d have been intro duced in order to describe systematical uncertainties and are the nuisance parameters Each of the four parameters has a central value and systematical error The central values for all of the four parameters have to be always defined They are called signal normalization a signal tilt calibration b background normalization c and background tilt calibration d The default values are a 1 b 0 c notassigned d 0 9 29 Thus for the background normalization c the value has to be specified in either case The values for the normalization and the values of tilt calibration are always regarded as a pairs i e they are given in the form normalization tilt The errors are treated in the same way For example we have signalerror 0 001 0 01 backgroundcenter 0 1 0 0 backgrounderror 0 001 0 01 There is no signalcenter in this definition since by default the central value for the signal normalization is 1 and the central value for the tilt calibration is 0 The user has the possibility to choose the set of nuisance parameters which are minimized over This choice is specified with the error dimension variable and the different
66. e no spectral information is used The error dimension 7 spectrum only leaves the normalization free oa Ce x and therefore only the spectral information is used As a consequence the settings for the normalization error will be ignored designated with the symbol oo signalerror 0 001 0 01 backgroundcenter 0 1 0 0 backgrounderror 0 001 0 01 errordim_sys_off 2 errordim_sys_on 0 energy_window 4 0 50 0 9 7 Version control in AEDL files In order to avoid problems which come from different versions of GLoBES and AEDL files it is possible to use in each AEDL file a version number For example it may correspond to the minimum version number of the GLoBES package with which it works Set the version by version 1 8 1 This information can be accessed by the versioning functions as described in Sec 2 5 86 CHAPTER 9 Experiment definition with AEDL 87 Chapter 10 Testing amp debugging of AEDL files AEDL is a powerful language to describe a variety of different experiments This chapter demonstrates how to test an AEDL file in order to check if it really describes a given experiment For this application the GLoBES package contains the program globes It can either be regarded as an AEDL debugger or as a simple command line oriented tool to convert the rather abstract AEDL experiment description into more accessible event rates 10 1 Basic usage of the globes binary The globes binary
67. e double norm double tilt writes the background errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 16 int glbSetBGCenters int exp int rule double norm double tilt sets the background centers of experiment exp and rule rule to norm normalization center and tilt tilt calibration center Function 7 17 int glbGetBGCenters int exp int rule double norm double tilt writes the background centers of experiment exp and rule rule to norm normaliza tion center and tilt tilt calibration center As usual all these functions return 1 if they were not successful 7 3 External parameters in AEDL files Using external parameters in AEDL files is a very powerful feature to change experiment parameters at running time which require that the experiment be re initialized For exam ple one can change the energy resolution function or the number of energy bins However in some cases there might be complications such that the number of pre or post smearing efficiencies does not correspond to the number of energy bins anymore Therefore this feature needs to be used with care In order to use external parameters in AEDL files one simply introduces them For example an energy resolution function energy EnergyResolution1 lt type 1 sigma_e myres 0 0 might be defined in AEDL where the energy resolution is proportional to myres x energy In order to use the
68. e one can obtain a result within about 10 to 30 seconds on a modern computer which means that the complete measurement precision for one fixed true parameter set can be obtained in as much as 10 to 15 minutes One can easily imagine that such a minimizer makes more sophisticated applications pos sible with the help of overnight calculations such as showing the dependencies on the true parameter values This approach also has one major disadvantage There is no such thing as a global minimization algorithm or even an algorithm which guarantees to find all local minima of a function In practice this means using a local minimizer one may end up in an unwanted local minimum and not in the investigated possibly global one or one may miss a local minimum which affects the results The only way out of this dilemma is to use some heuristic approach t e although one can not guarantee anything one can use schemes which work in most cases and announce their failure loudly In order to use such a heuristic some analytical or numerical knowledge on the topology of the fit manifold is necessary With this knowledge it is possible to obtain an approximate position for each local minimum and thus to start the local minimizer close enough to the investigated minimum Fortunately this can be done quite straightforward in most cases since the structure of the neutrino oscillation formulas does not cause very complicated topologies of the fit manifolds Especial
69. e context describes wether this name belongs to a rule channel flux energy or cross type environment exp is the number of the experiment and can not be GLB_ALL It returns either the index in case of success or 1 in case the name was not found 44 CHAPTER 6 Obtaining low level information Function 6 4 const char glbValueToName int exp const char context int value Converts a C index given as argument value into the corresponding AEDL name The variable context describes wether the index belongs to a rule channel flux energy or cross type environment exp is the number of the experiment and can not be GLB_ALL It returns either the name in case of success or NULL in case the name was not found The returned string must not be modified 6 3 Event rates One can also return event rates in GLoBES but this feature requires some knowledge about the experiment definition In fact many of these functions are very advanced which means that the reader who wants to use them should be familiar with Secs 9 4 and Sec 9 6 of the AEDL manual GLoBES currently supports rule based and channel based event rate functions where the information is in written into a file or returned in a list The rule based functions are Function 6 5 int glbShowRuleRates FILE stream int exp int rule int pos int effi int bgi int coeffi int signal prints the binned rule rates as list with energy and event rate to the file stream either an open file or stdou
70. e place counts as distribution of the source code even though third parties are not compelled to copy the source along with the object code 4 You may not copy modify sublicense or distribute the Program except as expressly provided under this License Any attempt otherwise to copy modify sublicense or distribute the Program is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in full compliance 5 You are not required to accept this License since you have not signed it However nothing else grants you permission to modify or distribute the Program or its derivative works These actions are prohibited by law if you do not accept this License Therefore by modifying or distributing the Program or any work based on the Program you indicate your acceptance of this License to do so and all its terms and conditions for copying distributing or modifying the Program or works based on it 6 Each time you redistribute the Program or any work based on the Program the recipient au tomatically receives a license from the original licensor to copy distribute or modify the Program subject to these terms and conditions You may not impose any further restrictions on the recipi ents exercise of the rights granted herein You are not responsible for enforcing compliance by
71. e simulated data are computed glbSetOscillationParameters true_values glbSetRates Ae CODE a ER Free parameter vector s glbFreeParams true_values exit 0 2 1 Initialization of GLoBES 15 Experiment Filename Short description Ref Conventional beams MINOS MINOS glb MINOS exp 5 yr running time 3 OPERA OPERA gIb OPERA exp 5 yr running time 3 ICARUS ICARUS glb ICARUS exp 5 yr running time 3 First generation superbeams T2K JHFSKnew glb J PARC to Super K 5 yr v running 4 JHFSKantinew glb J PARC to Super K 5 yr v running 4 JHFSKcomb glb Same but 1 25 yr v and 3 75 yr v running 4 NOVA NUMI9 glb NuMI OA 9km 712km 5 yr v running 4 NUMI9anti glb NuMI OA 9km 712km 5 yr v running 4 NUMI9comb glb NuMI OA 9km 712km 1 43 yr v and 4 3 97 yr V running NUMI12 g1b NuMI OA 12km 712km 5 yr v running 4 NUMI12anti glb NuMI OA 12km 712km 5 yr v running 4 NUMI12comb glb NuMI OA 12km 712km 1 43 yr v and 4 3 97 yr v running Superbeam upgrade J PARC HK JHFHKA11 g1b J PARC to Hyper K 2 yr v and 6 yr po 5 running Neutrino factories NUFACT I NuFact1 glb Initial stage NF 2x2 5 yr running time 5 each pol Mpe 10kt Prg 0 75 MW NUFACT II NuFact2 glb Advanced stage NF 2x4 yr running time 5 each pol Mpe 50kt Prg 4 MW Reactor experiments REACTOR I Reactori glb Small reactor exp 400 t GW yr 6 REACTOR II Reactor2 glb Large reactor exp
72. ed to do unusual things to compile the package please try to figure out how configure could check whether to do them and mail diffs or instructions to globes ph tum de so they can be considered for the next release If at some point config cache contains results you don t want to keep you may remove or edit it CHAPTER GLoBES installation 95 The file configure in is used to create configure by a program called autoconf You only need configure in if you want to change it or regenerate configure using a newer version of autoconf The simplest way to compile this package is 1 cd to the directory containing the package s source code and type configure to configure the package for your system If you re using csh on an old version of System V you might need to type sh configure instead to prevent csh from trying to execute configure itself Running configure takes awhile While running it prints some messages telling which features it is checking for It also prints a reminder for things to do after installation 2 Type make to compile the package 3 Type make install to install the programs and any data files and documentation 4 You can remove the program binaries and object files from the source code directory by typing make clean To also remove the files that configure created so you can compile the package for a different kind of computer type make distclean There is also a make maintainer clean target but that is
73. efined before The last step is to encapsulate the channels into a rule rules rule rule1 lt signal 0 45 appearance signalerror 0 001 0 0001 background 1 0e 05 disappearance backgroundcenter 1 0 0 backgrounderror 0 05 0 0001 errordim_sys_on 0 errordim_sys_off 2 energy_window 4 0 50 0 The signal refers to the signal in our experiment We use the above defined channel named appearance with an constant overall efficiency of 0 45 The signal error variable has two components The first one is the normalization error of the signal here 0 1 The second one refers to the energy calibration error of the signal which is defined in Sec 9 5 The background variable specifies the composition of the beam background In this sim plified case we use the fraction 1 10 of the channel named disappearance i e the muon neutrinos with a mis identified charge The background center variable allows to rescale the total background contribution from all background components simultaneously It is only useful if there is more than one background component otherwise it is usually 1 The background error variable is defined such as the signal error variable i e we have a 5 background uncertainty and a very small energy calibration error The error dimension variable errordim_sys_X selects how the systematical errors are treated cf Table 9 2 The here defined experiment represents a first sim
74. either by using the option p on a call by call basis or by setting the environment variable GLB_CENTRAL_VALUES globes p 0 55 0 0 785 0 0 0008 0 0025 globes parameters 0 55 0 0 785 0 0 0008 0 0025 For example GLB_CENTRAL_VALUES can be defined within the shell session or in the shell profile export GLB_CENTRAL_VALUES 0 55 0 0 785 0 0 0008 0 0025 Furthermore it is possible to switch off oscillations with the N option and to switch them on again with 0 the default The effect of N is the same as to use NOSC_ in all oscillation channels Thi feature is useful if one wants to normalize an expriment flux if the number of un oscillated events is given The AEDL parser and interpreter have basically three levels of messages to the user Warnings errors and fatal errors Fatal errors are always reported and lead to a program exit with status 1 Usually only errors and no warnings are reported The verbosity level can be chosen by the v option where v1 is default e only errors and fatal errors are reported The level v0 corresponds to reporting fatal errors only and v2 will print warnings in addition to fatal errors It is recommended to test any new glb file with v2 to check the warnings at least once and to decide whether there is a problem to be fixed With v3 all files read by globes are displayed together with their path and with v4 all files which have been attempted to be read are shown These t
75. eneral Public License 0 This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License The Program below refers to any such program or work and a work based on the Program means either the Program or any derivative work under copyright law that is to say a work containing the Program or a portion of it either verbatim or with modifications and or translated into another language Hereinafter translation is included without limitation in the term modification Each licensee is addressed as you Activities other than copying distribution and modification are not covered by this License they are outside its scope The act of running the Program is not restricted and the output from the Program is covered only if its contents constitute a work based on the Program independent of having been made by running the Program Whether that is true depends on what the Program does You may copy and distribute verbatim copies of the Program s source code as you receive it in any medium provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty keep intact all the notices that refer to this License and to the absence of any warranty and give any other recipients of the Program a copy of this License along with the Program You m
76. eral GLoBES uses the six independent oscillation parameters 612 013 923 dcp Am3 Am3 as well as the matter density scaling factor f of each experiment Thus there are six plus the number of experiments parameters determining the rate vectors Using the matter density scaling factors in addition to the oscillation parameters will allow the simulation of the correlations with matter density uncertainties In this approach the matter density profile normalization p can be treated as parameter to be measured by the experiment where an external precision given by observations is imposed typically up to 5 For this section it is important to keep in mind that there are more parameters than just the oscillation parameters determining the simple y However as we have described in the last section the mechanism for the matter density scaling factors is hidden in the definition of glb_params Each of the scaling factors is initially set to 1 0 Therefore for the calculation of x with systematics only we do not have to care about the matter density scaling factors Keeping all oscillation parameters and matter density scaling factors fixed one can use the following functions to obtain the total x of all specified oscillation channels including systematics Function 3 1 double glbChiSys const glb_params in int exp int rule returns the x for the fixed oscillation parameters in the experiment number exp and the rule number rule For all exp
77. ergy variable E and a set D F F for the flavor variable F In general D E E F also depends on the incident neutrino flavor F as well as D F F E depends on the in cident neutrino energy E These sets of mapping functions usually are obtained from a full detector simulation and can be obtained by using as input distribution f x a delta distribution x zo In order to implement a experiment definition including various sources of systematical errors we use several abstraction levels The first level is the so called channel which is the link between the oscillation physics and the detection properties for a specfific os cillation pattern cf Fig 8 2 A channel specifies the mapping of a specific neutrino flavor produced by the source onto a reconstructed neutrino flavor For example a muon neutrino oscillates into an electron neutrino and subsequently interacts via quasi elastic charged current scattering The measured energy and direction of the secondary electron in the detector then allows to reconstruct the neutrino energy The connection from the source flux of the muon neutrino via the probability to appear as a electron neutrino to its detection properties such as cross sections and energy smearing is encapsulated into the channel The channels are the building blocks for the so called rules In general a rule consists of one or more signal and background oscillation channels which are nor
78. eriment In many cases even parameter changes such as the number of bins require the recompilation of the source code However such a technique soon reaches its limits when the simulated experiments are rather complex or more than one type of experiment is studied simultaneously Furthermore it is very difficult to verify the correctness of the obtained results since every time a new piece of code is added to deal with a new experiment type new errors will be introduced Thus a general and flexible experiment description language is needed The description of a neutrino experiment can be split into three parts Source oscillation and detection The neutrino sources within GLoBES are assumed to be stationary point sources where each experiment has only one source This restricts the classes of neutrino sources which can be studied with GLoBES e Experiments using many point like sources can only be approximated One example are reactor experiments using many distant reactor blocks e Geometrical effects of a source distribution such as in the sun or the atmosphere can not be described e Sources with a physically significant time dependency can not be studied such as supernov amp It is however possible to study beams with bunch structure since the time dependence of the neutrino source is physically only important to suppress backgrounds 58 CHAPTER 8 Getting started The description of the neutrino oscillation physics is at
79. eriments or rules use GLB_ALL as parameter value Note that the result of glbChiSys for all experiments or rules corresponds to the sum of all of the individual glbChiSys calls This equality will not hold for the minimizers in the next sections anymore An example how to use glbChiSys can be found on page 24 The treatment of systematics in GLoBES is performed by the so call pull method with the help of auxiliary systematics parameters They are taken completely uncorrelated among different rules and treated with simple Gau ian statistics In general a rule is a set of signal and background event rates coming from different oscillation channels where the event rates of all rule contributions are added For more details of the rule concept see Part II of this manual and for the treatment of systematics see Sec 9 6 24 CHAPTER 3 Calculating x with systematics only Example Correlation between sin 2013 and dcp A typical and fast application for glbChiSys is the visualization of two parameter correlations using systematics only For example to calculate the two parameter cor relation between sin 26 3 and dcp at a neutrino factory one can use the following code excerpt from examplei c Initialize parameter vector s and compute simulated data glbDefineParams true_values theta12 thetal3 theta23 deltacp sdm 1dm glbDefineParams test_values theta12 thetal3 theta23 deltacp sdm 1dm glbSetOscillationParameters true_values
80. ert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works in or on a volume of a storage or distribution medium is called an aggregate if the copyright resulting from the compilation is not used to limit the legal rights of the compilation s users beyond what the individual works permit When the Document is included in an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on printed covers that bracket the whole aggregate 8 TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Document under the terms of section 4 Replacing Invariant Sections with translations requires special permission from their copyright holders but you may include translations of some or all Invariant Sections in addition to the original versions of
81. es at bin level are mainly determined by optimizing the performance of the experiment Analysis level On the analysis level an energy window can be defined within each rule For details see next chapter In general the energy smearing happens between the sampling point and bin levels which means that the energy smearing matrix will have sampling_points columns and bins rows As illustrated in the figure an interesting feature in combination with the chan nels are pre and post smearing effects Pre smearing effects are taken into ac count on the sampling point level and post smearing effects on the bin level Ex amples for these effects are energy dependent efficiencies and non beam back grounds Efficiencies are multiplicative factors whereas backgrounds are added to evaluated at emin and emax respectively 9 5 Energy resolution function 77 the event rates These components can be introduced before or after the inte gration in Eq 9 9 is done If they are introduced before we call them pre_smearing_efficiencies or pre_smearing_background If they are introduced af ter we call them post_smearing_efficiencies or post_smearing_background Note that pre smearing components are always a function of the incident neutrino energy E Thus there have to be as many elements as there are sampling points Examples for pre smearing quantities are non beam backgrounds such as from geophysical neutrinos The post smearing comp
82. eters in experiment definitions can be changed at running time For example we have introduced in Sec 2 2 possibilities to change the integrated luminosity which consists of source power running time and target mass In this chapter we discuss more sophisticated experiment changes However since GLoBES computes a lot of infor mation only once when an experiment is loaded many parameters can not be changed at running time For example the energy resolution function or the number of bins are used to compute the smearing matrix already at the initialization of the experiment which saves a lot of computation time for most applications In Sec 7 3 we introduce a mechanism how one can even change these AEDL parameters during running time 7 1 Baseline and matter density profile In order to change the baseline of an experiment it is important to keep in mind that each experiment has a profile type defined in the AEDL file average density PREM profile with a given number of steps or arbitrary profile One can check the currently used profile type with Function 7 1 int glbGetProfileType int exp returns the matter density profile type of experiment exp For each profile type one can easily change the baseline with glbSetBaselineInExperiment where the average density or the PREM profile are re computed or the steps in the arbitrary profile are re scaled If this behaviour is not the desired one one has to use glbSetProfilDataInExperiment
83. g low level information Function 6 15 void glbResetRateStack resets the rate stack used for the lists re turned from glbGetChannelRates or glbGetUserData A code excerpt to show the channel rates may look like this double rates size_t length glbGetChannelRates amp rates amp length 0 0 GLB_PRE int i for i 0 i lt length i printf g n rates i glbResetRateStack Finally one can find the number of channels of an experiment Function 6 16 int glbGetNumberOfChannels int exp returns the number of channels of experiment exp 6 4 Fluxes and cross sections Another piece of low level information which can be returned by GLoBES are the numbers from the loaded fluxes and cross sections The following functions interpolate on the loaded fluxes and cross sections i e any value in the allowed energy range can be given as input Function 6 17 double glbFlux int exp int ident double E double distance int 1 int anti returns the flux of flux number ident of the experi ment exp for the flavor v and polarity anti 1 neutrinos 1 antineutrinos at the energy E and distance distance Function 6 18 double glbXSection int exp int ident double E int 1 int anti returns the cross section of experiment exp cross section number ident for the flavor v and polarity anti 1 neutrinos 1 antineutinos at the energy E 47 Chapter 7 Changing experiment parameters at running time Many of the param
84. h 100 matter density steps and print them 50 CHAPTER 7 Changing experiment parameters at running time double lengths double densities glbStaceyProfile 7500 100 amp lengths amp densities int i for i 0 i lt 100 i printf g g n lengths i densities i glbSetProfileDataInExperiment 0 100 lengths densities free lengths free densities 7 2 Systematics Changing the systematics at running time can be useful to investigate the impact factors affecting the measurement In GLoBES the systematics is defined rule based i e each rule has its own systematics In addition AEDL requires that it has to be defined in each rule what Systematics on and Systematics off means Therefore it is usually very simple to switch the systematics on and off Function 7 9 int glbSwitchSystematics int exp int rule int on_off switches the systematics in experiment exp and rule rule on on_off is GLB_ON or off on_off is GLB_OFF For the experiment or rule index one can also use GLB_ALL In the example on page 51 the application of glbSwitchSystematics is demonstrated to show the impact of systematics correlations and degeneracies The error dimension for the definition see Sec 9 6 can also be accessed directly with Function 7 10 int glbSetErrorDim int exp int rule int on_off int value sets the error dimension for systematics on on_off is GLB_ON or off on_off is GLB_OFF of experiment exp and rule
85. hat could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them 106 CHAPTER GNU Free Documentation License The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the notice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightfor wardly with generic text editors or for images composed of pixels generic paint programs or for drawings some widely available drawing editor
86. he guessed starting point might be quite far away from the real degeneracy the algorithm may in some cases find the original solution instead of the degeneracy which can be immediately seen from the output vector The input error for Am3 gives the algorithm a bias against the original solution However note that the input error must not be too small in order to avoid a significant contribution of the prior to the final x Alternatively one could once again run glbChiAll with the located minimum as in vector and Am kept free Finding degeneracies with multiple experiments For multiple experiments it turns out to be useful to locate the degeneracies for individual experiments first Then all of the found degeneracies below the threshold can be tested for the combi nation of all experiments Finally note that any degenerate solution below the confidence level threshold which can not be located makes the result appear better than it actually is Thus one should be careful with the determination of the degenerate solutions in order to find all of them The discussed figure on page 40 is produced by glbChiSys and thus only represents a section through the fit manifold For the projection including correlations one may rather want to use glbChiThetaDelta 42 CHAPTER 5 Locating degenerate solutions 43 Chapter 6 Obtaining low level information In this chapter we discuss possibilities to obtain low level information in GLo
87. he list 1 2 3 1 2 3 The delimiters can be set by L M and R as in the following example globes Su R n Middle L Here n is the escape sequence in the shell for ANSI C like characters such as linefeed n The above example produces a a two column file such as 1 0 0 12 1 2 0 14 1 3 0 18 where the first column is the central energy of the bin or the sampling point and the second column gives the event rate Usually the output is a concatenation of many such two columns tables where each rule part or channel part has its own table Thus one can by using u and user defined delimiters construct many different output formats AEDL external variable substitution Some glb files use external AEDL variables in order to allow special purpose studies such as the energy resolution dependence If the external variables are not explicitely specified they are interpreted by the parser as zeros Thus it is impossible to properly parse any files with globes which contain such undefined variables Hence there is the possibility to define AEDL variables by using the define option D A call such as globes DBASELINE 3000 would define the AEDL variable BASELINE to be 3000 91 Acknowledgments We would like to thank Martin Freund who wrote the very first version of a three flavour matter profile treatment many years ago PH is especially thankful for the invaluable advice of Thomas Fischbacher o
88. her with the energy resolution function in the next section At least in the absence of sterile neutrinos 3In case the backgrounds have a sizeable dependence on the oscillation parameters they carry infor mation on the oscillation parameters and are therefore more like a signal 74 CHAPTER 9 Experiment definition with AEDL 9 5 Energy resolution function The definition and implementation of the energy resolution function is rather sophisticated in GLoBES In particular the choice of the proper parameters depends on the experiment and the frequencies of the involved neutrino oscillations This choice also greatly influences the speed of the calculation In this section we first discuss the principles of the energy smearing where it is as sumed that the reader is familiar with Sec 9 4 Then we introduce an automatic energy smearing algorithm which is fairly simple to understand and applicable to most beam based experiments In most cases the reader may want to continue to the next section after reading these two subsections In the third subsection we describe a more elaborate and slower smearing algorithm which can be used together with rather fast neutrino os cillations compared to the bin size such as for solar reactor experiments to avoid aliasing effects Eventually we show how one can use a manual smearing matrix instead of using one of the implemented algorithms 9 5 1 Introduction and principles The energy resolution
89. here first of all a short GLoBES tour is given in Chapter 1 in order to have an overview over GLoBES After that the user interface is successively introduced from very basic to more sophisticated functions Eventually it is demonstrated how one can change many experiment parameters at running time such as baseline or target mass and how one can obtain low level information We recommend that everybody interested in GLoBES should become familiar at least with the concepts in Chapter 1 and some of the examples on the boxed pages The examples can be directly compiled from the respective directory in the GLoBES software package In Part II of the manual AEDL is described After an introductory chapter all functions are defined in greater detail This part might be more interesting for the experimental users who want to modify or create AEDL files A useful tool in this context is the software program globes which returns event rates and other information for individual AEDL files without further programming For example flux normalizations can with this tool be easily adjusted to reproduce the event rates of a specific experiment It is described in the last chapter of Part II Note All examples for application software in C do require a C compiler to be prop erly compiled For pedagogical reasons variable declarations are done at that place where the variable is needed for the first time which is at variance with C syntax but not with C s
90. hin the appropriate type of environment In many cases they have a special syntax such as channel If you want to have several experiments in one file separate the different experiments by NEXT This command resets the counters for channels rules fluxes cross section and energy res olution environments All variables have their scope limited by either GLoBES NEXT or EOF This allows a consistent treatment of various experiments in one file As another feature of AEDL one can use include files with the include command Includes can be nested up to MAX_INCLUSION_DEPTH which is currently set to 10 Error reporting works for nested includes too The included file is not required to begin with GLoBES to facilitate cut and paste include file_1 With this include mechanism one can use constructions such as include NuFact gls NEXT include JHFHK gls in order to initialize a combined analysis of the experiments defined in the files NuFact gls and JHFHK gls Note that one has to use quotation marks for filenames in AEDL Even if one uses the automatic variable CC in both experiments but the cross section data are different for example because of different target nuclei the correct cross section data will be applied to each of the experiments Note that alternatively one can also load both files successively by two separate calls of glbInitExperiment Furthermore one can define constants such as Pi 3 141
91. iment to this list one can use the function glbInitExperiment Function 2 2 int glbInitExperiment char inf glb_exp in int counter adds a single experiment with the filename inf to the list of currently loaded experiments The counter is a pointer to the variable containing the number of experiments and the experiment in points to the beginning of the experiment list The function returns zero if it was successful Normally a typical call of glbInitExperiment is Note that the global variable glb_num_of_exps must not be modified by the user 3if the verbosity level is set accordingly 2 1 Initialization of GLoBES 17 Quantities Examples Units Angles 013 912 023 dcp Radians Mass squared differences Am3 Am3 eV Matter densities pi g cm Baseline lengths L km Energies E GeV Fiducial masses MDet t reactor exp or kt accelerator exp depends on experiment definition Time intervals tain yr Source powers Psource Useful parent particle decays yr Neutrino factory G Beam GW thermal power reactor exps or MW target power superbeams depends on flux definition Cross sections E occ E 10738 cm GeV Table 2 2 Quantities used in GLoBES examples of these quantities and their standard units in the application software glbInitExperiment NuFact glb amp glb_experiment_list 0 amp glb_num_of_exps In this case the experiment in the file NuFact glb is added to the internal global list of experiments
92. imum Then we clear the experiment list and load the new experiments fprintf stream nNOW TWO EXPERIMENT SETUP NuFact at 3000km NuFact at 7500km n n glbClearExperimentList glbInitExperiment NuFact glb amp glb_experiment_list 0 amp glb_num_of_exps glbInitExperiment NuFact glb amp glb_experiment_list 0 amp glb_num_of_exps Output NOW TWO EXPERIMENT SETUP NuFact at 3000km NuFact at 7500km Then we need to change the baseline of the second experiment where we set the density to the average density of this baseline double lengths double densities glbAverageDensityProfile 7500 amp lengths amp densities fprintf stream Magic baseline length 4g Density g n n lengths 0 densities 0 glbSetProfileDataInExperiment 1 1 lengths densities free lengths free densities CHAPTER 1 A GLoBES tour 9 Output Magic baseline length 7500 Density 4 25286 Now we can re initialize our parameter vectors again true_values glbAllocParams fit_values glbAllocParams starting values glbAllocParams input_errors glbAllocParams minimum glbAllocParams glb_params minimum2 glbAllocParams In addition we repeat the procedure for the simulated rates and the fit parameter vector glbDefineParams true_values theta12 thetal3 theta23 deltacp sdm 1dm glbSetOscillationParameters true_values glbSetRates glbCopyParams true_values fit_v
93. in the plane but it does appear at the real minimum The two sections through the fit For a exact definition of inverted hierarchy see page 19 40 CHAPTER 5 Locating degenerate solutions Example Finding the sgn Am3 degeneracy In many cases one can find the exact position of the sgn Am3 degeneracy with glbChiAll where one starts the local minimizer at the suspected position and let it run into the minimum The following code excerpt corresponds to finding the degenerate solution for the example on page 24 and it is from example3 c Set starting vales to suspected position at opposite sign of ldm glbDefineParams starting_values theta12 thetal3 theta23 deltacp sdm ldm Set input errors for external input where some information on ldm is imposed in order to avoid falling into the right sign solution glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 1dm 3 glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues starting_values glbSetInputErrors input_errors Localize degenerate solution by minimization over all parameters double CL glbChiAll starting_values deg_pos GLB_ALL Now CL is the chi2 of the deg solution and deg_pos the position Using ent_pos to obtain a section of the degeneracy in the sin 2013 cp plane cf example3 c one can plot it as a contour plot in addition to the original solution 2 d o f gray curves cp Degrees 10
94. is installed together with the library but into the directory prefix bin In order to use the globes utility this directory has to be in the path of the shell used to call the program As an argument globes takes a glb file While parsing it it prints any warnings and errors which have occured during reading the file Then it uses the experiment description in the file to compute the event rates at a certain point in parameter space Finally it displays the result based on the options used to call globes The options of globes follow the GNU standard Thus there is a help option to display all other options together with short descriptions Calling globes without any options and with a glb file as argument produces an event summary at rule level In this case the full experiment description in the file is taken into account 2 e all efficiencies backgrounds and energy resolution effects Thus the returned event rates are the ones which will be actually used to compute the x later By default the oscillation parameters used to calculate the transition probability are sin 2015 0 8 Am 7 10 eV sin 2603 1 0 Am 310 eV 6 0 sin 2013 0 1 10 1 This is automatically the case if no options are given to configure and make install was executed with root privilege i e a standard installation was done 88 CHAPTER 10 Testing amp debugging of AEDL files Of course it is possible to change these default values
95. ison of fit manifold sections and projections for the solutions where the absolute minimum x is larger than zero i e degeneracies other than the true solution In this case the sections and projections are not comparable if not corrected by the prior contributions where the correction can be obtained as the x difference at the minimum For example projecting the sgn Am3 degeneracy onto the 13 cp plane and comparing it with the section all other parameters fixed the section region would in many cases be larger than the projection region if the priors are not added to the section At the true solution this problem usually does not occur because the prior contributions are close to zero 3 Currently GLoBES only supports Gaufian priors for the individual oscillation pa rameters Especially for the solar parameters this is only an approximation since they are imposed on 4 2 and not on sin 2012 sin 2012 Am3 or sin 12 Later versions of GLoBES may include more alternatives 4 3 Projection onto the sin 2013 or dcp axis The projection onto the sin 2013 or dcp axis is performed by fixing sin 20 3 or dcp and minimizing the y function over all free fit parameters and the matter densities We illustrate this method at the example of the projection of the two dimensional manifold in the sin 2013 cp plane onto the sin 26 3 axis in Fig 4 1 In this figure the left hand plot shows the correlation in the sin 26 3 dcp plane c
96. ith correlations for 7500km Ag n chi2b glbPrintParams stream minimum chi2sum glbChiTheta fit_values minimum GLB_ALL fprintf stream nchi2 with correlations for combination Ag n chi2sum glbPrintParams stream minimum fprintf stream nThe sum of the two chi2s is g whereas the total chi2 is g n n chi2 chi2b chi2sum Output chi2 with correlations for 3000km 2 1038 0 542002 0 0193698 0 747915 1 77688 6 66156e 05 0 00200817 1 00434 1 Iterations 1693 chi2 with correlations for 7500km 1 08421 0 557356 0 0193698 0 771359 4 77751 7 00762e 05 0 00200105 1 1 01517 Iterations 661 chi2 with correlations for combination 3 90835 0 544432 0 0193698 0 770175 1 78502 6 61621e 05 0 00200303 1 00431 1 03679 Iterations 1636 The sum of the two chi2s is 3 18801 whereas the total chi2 is 3 90835 Now find the sgn Am3 degeneracies for both individual experiments and test if they are still there in the combination of the experiments CHAPTER 1 A GLoBES tour 11 glbDefineParams input_errors theta12 0 1 theta13 theta23 deltacp sdm 0 1 1dm 3 glbDefineParams starting _values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues starting_values glbSetInputErrors input_errors chi2 glbChiAll starting_values minimum O0 fprintf stream chi2 at minimum L 3000km g n chi2 glbPrintParams stream minimum chi2b glbChiAl
97. l flavor the cross sections and the energy resolution function In order to refer to flux cross sections and energy resolution functions they have to be defined before with their name in the respective environments Thus a simple definition of a channel is channel channel_1 lt channel flux muon muon cross energy gt It is also possible to define a channel as no oscillation by using the prefix NOSC_ in either the initial flavour or the final flavour like this channel channel_1 lt channel flux NOSC_muon muon cross energy gt In this case all diagonal probabilities Paa are unity and all off diagonal probablities Pag are zero This is for instance useful for neutral current events since these do not depend on any oscillation parameters The channels marked as NOSC_ are already computed by glbSetRates and do not have to be recomputed in the subsequent fit which calls the undocumented function glbSetNewRates Therefore this feature can be used to speed up the rate computation considerably especially in cases where a large set of channels exist which are only used for the computation of backgrounds Usually it is an excellent approximation to treat backgrounds as if they were not affected by oscillations Note that the energy environment will be described in the next section In addition one can define pre and post smearing effects together with the channels which will also be introduced toget
98. l of the earth profiletype 1 70 CHAPTER 9 Experiment definition with AEDL profiletype Additional variables Description baseline Average density constant baseline densitysteps PREM profile with given number of equidistant steps lengthtab densitytab Arbitrary profile table of layer thick nesses table of densities Table 9 1 Different matter density profiles which can be used with GLoBES If your using this option please cite reference 2 For a better approximation of the realistic earth matter density profile one can use an arbitrary number of equidistant steps of the PREM profile profiletype 2 densitysteps 20 Note that the value of densitysteps is time critical since the computation time of oscil lation probabilities is directly proportional to the number of layers As a third possibility one can specify the matter density profile manually with a list of thicknesses and densi ties of the matter density layers This example uses two density steps with two different densities profiletype 3 densitytab 2 8 3 5 lengthtab 1000 0 2000 0 It is important that both lists have the same length and that the thicknesses given in lengthtab add up to the length of the baseline which does not have to be explicitely specified anymore In addition matter densities are always given in g cm This approach can also be used for a constant matter density profile with a specific matter density profiletype
99. l starting_values minimum2 1 fprintf stream nchi2 at minimum L 7500km g n chi2b glbPrintParams stream minimum 2 chi2 g1lbChiAll minimum minimum GLB_ALL fprintf stream nchi2 for combination at minimum of Exp 1 Ag n chi2 glbPrintParams stream minimum chi2b glbChiAll minimum2 minimum2 GLB_ALL fprintf stream nchi2 for combination at minimum of Exp 2 Ag n chi2b glbPrintParams stream minimum2 Output chi2 at minimum L 3000km 6 71794 0 591497 0 0257396 0 729058 1 11537 7 98867e 05 0 00206005 0 970499 1 Iterations 2104 chi2 at minimum L 7500km 47 1013 0 590347 0 0018489 0 768372 0 984827 8 23415e 05 0 00204588 1 0 780995 Iterations 1270 chi2 for combination at minimum of Exp 1 70 6353 0 607988 0 0165985 0 767682 1 41422 8 44573e 05 0 00204853 0 96147 1 1831 Iterations 1549 chi2 for combination at minimum of Exp 2 70 6357 12 CHAPTER 1 A GLoBES tour 0 608454 0 0165823 0 767757 1 41481 8 43864e 05 0 00204853 0 961129 1 18304 Iterations 1447 Finally we have to free the parameter vectors again glbFreeParams true_values glbFreeParams fit_values glbFreeParams starting values glbFreeParams input_errors glbFreeParams minimum glbFreeParams minimum 13 Chapter 2 GLoBES basics In this first chapter of the user s manual we assume that the GLoBES software is readily installed on your computer system For the installation see Ap
100. lation parameter vectors 919 413 023 dcp Am Am3 the parameter type glb_params is used In general this type is often transferred to and from GLoBES functions Therefore the memory for these vectors has to be reserved allocated before they can be used and it has to be returned freed afterwards GLoBES functions usually use the pointers of the type glb_params for the input or output to the functions As an input parameter the pointer has to be created and point towards a valid parameter struc ture where the oscillation parameters are read from As an output parameter the pointer has to be created too and point towards a structure which will contain the return values will be written to This parameter transfer concept seems to be very sophisticated but as we will see in the next chapters it hides a lot of complicated parameter mappings which otherwise need to be done by the user For example not only the oscillation parameters are stored in the pointer structure but also information on the matter densities of all of the initialized experiments Since GLoBES treats the matter density as a free parameter known with some external precision to include matter density uncertainties the minimizers also use fit values and external errors for the matter densities of all loaded experiments More precisely the matter density profile of each experiment i is multiplied by a scaling factor Pi which is stored in the density information of glb_par
101. le it can be assumed as fixed safely The inclusion of external input in GLoBES is done by the use of Gau ian priors We assume that an external measurement has determined the measured parameter to be at the central value which we call starting value with a lo Gau ian error which we call input error The explicit definition of these priors will be shown in the next section 4 2 The treatment of external input It is one of the strengths of the GLoBES software to use external input in order to reduce the extension of the fit manifold with the knowledge from external earlier measurements The treatment of external input is done by the addition of Gau ian so called priors to the systematics minimized y function For example for the matter density one obtains as the final projected x7 after minimization over the matter density scaling factor f xh min vo e 4 This example is a very simple one since in fact the minimization is simultaneously per formed over all priors and free oscillation parameters In Eq 4 1 6 is the starting value of the prior and a the lo absolute half width input error Thus it is assumed that an external measurement has determined the matter density with a precision input error 0 at the central value f Usually the starting value is fixed at the best fit value and the input error to the 10 half width of the external measurement For the matter density is usually set to 1 0 corresponding to
102. least numerically relatively simple We use the evolution operator method 8 to compute the neutrino oscillation probabilities and divide the matter density profile into layers of constant matter density For each of these layers the Hamiltonian in matter is diagonalized in order to propagate the neutrino transition amplitudes Finally the transition probability is obtained by the absolute square of the total neutrino transition amplitudes Depending on the precision of the studied experiment this approach turns out to be precise enough in Earth matter even if only a small number matter density steps is used Since we allow an uncertainty of the matter density profile it is in fact in most cases sufficient to consider only one density step with the average matter density together with a matter density uncertainty 9 Note that this approach may not be applicable to quickly varying extraterrestrial matter density profiles While it is comparatively simple to define a general neutrino source and to compute the oscillation physics the general properties of a detector simulation are much more complicated The basic assumption in building an abstract detector description is linearity i e that two neutrino events do not interfere with each other Furthermore it is assumed that all information on the oscillation physics is given by the reconstructed flavor and energy of a neutrino event The term reconstructed implies that the well defined energy
103. ly the simulation of reactor experiments and conventional beams or superbeams is rather simple with purely numerical approaches Neutrino factories have especially for small values of 0 3 a much more complicated topology In this case results of the many analytical discussions of this issue can be used This means that one can implicitly use the analytical knowledge to obtain better predictions for the location of a minimum One can easily imagine that the used methods then also depend on the region of the parameter space In this manual we only use examples with a neutrino factory since some of these complications can be illustrated there Albeit the methods described here are neither complete nor will they work everywhere in the parameter space It is in any case up to the user to make sure that the results are what he she thinks Some more words of warning with respect to results obtained by projecting the x The results obtained this way are always only a upper bound on the value of the projected x function i e an undiscovered minimum decreases the value of the the projected x function If the value of the x function in the missed minimum is larger than the previously found ones it will not influence the value of the projected value Thus one can only run the danger to obtain a too optimistic solution if one does not find the other local minima appearing below the chosen confidence level Thus with this approach and proper usage it should n
104. m3 Am3 Am3 because with this defintion the absolute value of Am3 is unchanged and no new frequency is introduced Another piece of information will be returned from the minimizers cf Chapter 4 and transferred into the glb_params structure is the number of iterations used for the 20 CHAPTER 2 GLoBES basics minimization which is proportional to the running time of the minimizer In general the user does not need to access the elements in glb_params directly A number of functions is provided to handle these parameter structures Function 2 10 glb_params glbAllocParams allocates the memory space needed for a parameter vector and returns a pointer to it Function 2 11 void glbFreeParams glb_params stale frees the memory needed for a parameter vector stale and sets the pointer to NULL Function 2 12 glb_params glbDefineParams glb_params in double theta12 double thetal3 double theta23 double delta double dms double dma assigns the complete set of oscillation parameters to the vector in which has to be allocated before The return value is the pointer to in if the assignment was successful and NULL otherwise Function 2 13 glb_params glbCopyParams const glb_params source glb_params dest copies the vector source to the vector destination The return value is NULL if the assignment was not successful Function 2 14 void glbPrintParams FILE stream const glb_params in prints the parameters in in to the file stream
105. malized with efficiencies cf Fig 8 3 The event numbers from these channels are added before the Ay value is calculated t In addition each rule implements an independent systematics such as signal and background normalization errors Eventually each rule gives a Ay Note that in this manual the x and Ax are equal since for simulated data Ay 0 at the best fit point Thus we are using x and Ay as equal quantities 60 CHAPTER 8 Getting started eee Figure 8 3 General concept of a rule value and the total Ax of one experiment is obtained by adding the Ay s of all rules cf Fig 8 4 An example for a rule could look like this We want to detect electron neutrino appearance signal where the overall efficiency for quasi elastics electron neutrino events is 0 4 There is a fraction of 0 01 of all neutral current events which are mis identified as quasi elastic electron neutrino events background The neutral current fraction is only known within 10 background uncertainty and there is an energy scale uncertainty of 100 MeV energy calibration error All this systematics is independent of the other rules Thus a rule connects the event rates to the calculation of a Ay which properly includes systematical errors The resulting Ax is then the starting point for the oscillation physics analysis Note again that e Within each rule the event numbers are added e Within each rule the
106. matics 25 50 TestLibraryVersion 22 TestReleaseVersion 22 TotalRuleRate 44 VacuumProbability 43 ValueToName 44 65 VersionOfExperiment 22 XSection 46 115 116 API constants amp macros GLB_ALL 4 16 23 50 GLB_BG 44 45 GLB_DELTA_CP 20 GLB_DM_ATM 20 GLB_DM_SOL 20 GLB_EFF 45 GLB_FIXED 35 36 GLB_FREE 35 36 GLB_OFF 50 53 GLB_ON 50 53 GLB_POST 45 GLB_PRE 45 GLB_SIG 44 45 GLB_THETA_12 20 GLB_THETA_13 20 GLB_THETA_23 20 GLB_WO_BG 44 45 GLB_WO_COEFF 44 GLB_WO_EFF 44 45 GLB_W_BG 44 45 GLB_W_COEFF 44 GLB_W_EFF 44 45 GLB_ALL 16 CHAPTER Indices AEDL REFERENCE AEDL reference channel 71 73 NOSC_ 73 post_smearing_background 77 post_smearing_efficiencies 77 pre_smearing_ background 77 pre_smearing_ efficiencies 77 cross 70 cross_file 70 71 energy 74 81 energy 81 inverse_beta 79 sigma_function 78 standard 78 type 80 type 78 flux 68 builtin 68 flux_file 68 69 norm 68 parent_energy 68 power 68 stored_muons 68 time 68 rule 81 85 background 82 backgroundcenter 84 backgrounderror 84 energy_window 83 errordim 85 errordim_sys_off 84 errordim_sys_on 84 signal 82 signalerror 84 acos 66 asin 66 atan 66 baseline 69 bins 76 117 binsize 76 cos 66 densitysteps 69 densitytab 69 emax 76 emin 76 exp 66 filter_state 79 filter_value 79 include 65 lengthtab
107. mechanisms into the program and AEDL files to check whether e The program should only run with this specific version of GLoBES e The program can only run with a minimum version of GLoBES e The program can only run up to a certain GLoBES version The same holds for AEDL files For example some features may not be supported by earlier versions of GLoBES anymore The program can then check the version of the AEDL file and break if it is too old The functions in GLoBES for version control are Function 2 24 int glbTestReleaseVersion const char version returns 0 if the version string of the format X Y Z is exactly the used GLoBES version 1 if it is older and 1 if it is newer Function 2 25 int glbTestLibraryVersion const char version returns 0 if the version string of the format X Y Z is exactly the used GLoBES version 1 if it is older and 1 if it is newer Note that the library and GLoBES versions are not the same Function 2 26 const char glbVersionOfExperiment int experiment returns the version string of the experiment number experiment The version string is allocated within the experiment structure which means that it cannot be altered and must not be freed by the user 23 Chapter 3 Calculating x with systematics only Calculating a x value with or without systematics but no correlations and degeneracies is the simplest and fastest possibility to obtain high level information on an experiment In gen
108. n many design issues In addition we would like to thank Mark Rolinec for his help to translate the experiment descriptions into AEDL and for creating the illustrations in this manuscript Finally thanks to all the people who have been pushing this project for many years to the ones who have been continuing asking for the publication of the software and the referees of several of our papers for suggestions which lead to improvements in the software This work and the development of GLoBES have been supported by e Physik Department der Technischen Universit t M nchen e Max Planck Institut f r Physik e Sonderforschungsbereich 375 f r Astro Teilchenphysik der Deutschen Forschungsgemeinschaft e Studienstiftung des Deutschen Volkes 92 CHAPTER 10 Testing amp debugging of AEDL files 93 GLoBES installation The installation of GLoBES is highly automated and there should not be any problems on a decently up to date GNU Linux system The installation has however only been tested on a limited number of platforms mainly running with various versions of SuSE Linux Thus we would appreciate to know your experiences with the installation on different platforms Please send an e mail to lt globes ph tum de gt Prerequisites for the installation of GLoBES Besides the usual things such as a working libc you need to have gcc The GNU compiler collection gcc gnu org BLAS Basic Linear Algebra Subprograms www netlib org blas LA
109. nd what are minimized over Thus in comparison to glb_parans it does not take values for the parameters but flags GLB_FIXED or GLB_FREE For example the projection onto how one can include correlations 36 CHAPTER 4 Calculating y projections Function Purpose Parameters Result glbAllocProjection Allocate projection vector O glbFreeProjection Free projection vector stale glb_projection stale glbDefineProjection Assign projection vector in glb_projection in int theta12 int thetal3 int theta23 int delta int dms int dma glbCopyProjection Copy vector source to dest const glb_projection source glb_projection dest glbPrintProjection Print vector in to file stream FILE stream const glb_projection in glbSetProjectionFlag Set flag for oscillation parame glb_projection in int ter which in vector in to value flag int which flag glbGetProjectionFlag Return flag for oscillation pa const glb_projection rameter which in vector in in int which int flag glbSetDensity Set flag for density parameter glb_projection in int ProjectionFlag which in vector in to value flag int which flag glbGetDensity Return flag for density param const glb_projection ProjectionFlag eter which in vector in in int which int flag Table 4 1 Different functions handling the glb_projection type Flags are either GLB_FIXED or GLB_FREE The un shown return values of the Set and Define functions point either to the assigned vec
110. nguishing version number If the Document specifies that a particular numbered version of this License or any later version applies to it you have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the Free Software Foundation 110 CHAPTER GNU Free Documentation License 111 Bibliography 10 11 12 P Huber M Lindner and W Winter Simulation of long baseline neutrino oscillation experiments with GLoBES 2004 hep ph 0407333 F D Stacey Physics of the earth 2nd ed Wiley 1977 P Huber M Lindner M Rolinec T Schwetz and W Winter Prospects of accel erator and reactor neutrino oscillation experiments for the coming ten years 2004 hep ph 0403068 P Huber M Lindner and W Winter Synergies between the first generation JHF SK and NuMI superbeam experiments Nucl Phys B654 2003 3 29 hep ph 0211300 P Huber M Lindner and W Winter Superbeams versus neutrino factories Nucl Phys B645 2002 3 48 hep ph 0204352 P Huber M Lindner T Schwetz and W Winter Reactor neutrino experiments compared to superbeams Nucl Phys B665 2003 487 519 hep ph 0303232 R P Brent Algorithms for minimization without de
111. nitializes the library libglobes and has to be called in the beginning of each GLoBES program It takes the name name of the program as a string to initialize the error handling functions In many cases it is sufficient to use the first argument from the command line as the program name such as in example on page 14 The data files AEDL and supporting files needed by the examples are already in place 14 Example CHAPTER 2 GLoBES basics Using GLoBES with C Here comes the C code skeleton which is more or less common to all of our GLoBES examples include lt stdio h gt include lt stdlib h gt include lt math h gt include lt string h gt include lt globes globes h gt Include GLoBES library include myio h Include housemade I O routines If filename given write to file if empty to screen char MYFILE testX dat int i main int argc char argv glbInit argv 0 Initialize GLoBES library glbInitExperiment NuFact glb amp glb_experiment_list 0 amp glb_num_of_exps Initialize experiment NuFact glb Initialize housemade output function InitOutput MYFILE Format n Initialize parameter vector s glb_params true_values glbAllocParams Ik 1 Assign thetal2 thetal3 theta23 deltacp dm2solar dm2atm glbDefineParams true_values asin sqrt 0 8 2 asin sqrt 0 001 2 M_PI 4 M_PI 2 7e 5 2e 3 Th
112. nput files since in case they are distributed everybody will know how to correctly reference your work IV Contents How to use this manual I 1 2 User s manual A GLoBES tour GLoBES basics 2 1 Initialization of GLOBES Adie Sun era Hr a OR ES 2 2 Units in GLoBES and the integrated luminosity 2 3 Handling oscillation parameter vectors 4 2 4 Computing the simulated data 2 28 5 83 i OR ee oe es 2 0 Version c ntrol ee Sip ye nl ee La see nee Lae a a LA Ree LS Calculating y with systematics only Calculating projections how one can include correlations Ale VND EO CIC HOW et or ts cet Ze te u nh de IN a a S 4 2 The treatment of external input 4 3 Projection onto the sin 2013 axis or dcp axis 2 4 4 Projection onto any hyperplane Locating degenerate solutions Obtaining low level information 6 1 Oscillation probabilities 244 2 28 4 42 440 4 25 24 6 2 AEDLnames 0 0 0 000000 000 ee ee 6 3 Event T tes lt lt ote ete 8S eee PG ee Se eo ale eS 6 4 Fluxes and cross sections fe ow Se ww Ee ee et Changing experiment parameters at running time 7 1 Baseline and matter density profile 1 2 SOVELOMAICS ae 2a ahs Ie BARA eh ke eh eee a he ed 7 3 External parameters in AEDL files 0 13 13 18 19 21 22 23 27 21 29 31 35 39 43 43 43 44 46
113. nt the user to the references he she should to cite when using a particular cross section 9 4 Oscillation channels Channels in GLoBES represent an intermediate level between the pure oscillation physics given by the oscillation probability Pag and the total event rates composed of signal and background A channel describes the path from one initial neutrino flavor in the source to the event rates in the detector for one specific interaction type IT and final flavor Therefore a channel contains the description of the initial neutrino flavor its CP eigenvalue neutrino or antineutrino the detected neutrino flavor the interaction cross sections for the chosen interaction type and the energy resolution function of the detector Before we come to the definition of the channel in AEDL we introduce the general concept for the calculation of event rates The first step is to compute the number of events for each IT in the detector for each initial and final neutrino flavor and energy bin The second step is to include the detector effects coming from the insufficient knowledge in the event reconstruction These two steps combined lead to the differential event rate spectrum for each initial and final flavor and IT as seen by the detector which we call the channel In this section we focus on the first step i e we discuss the definition of the energy resolution function in the next section since this is a rather comprehensive issue C
114. o the respective axis Similarly one can project the fit manifold onto a plane such as the sin 2013 cp plane if one wants to show the allowed region in this plane with all the other parameter correlations included In practice this projection is very difficult a grid based method would need Neria function calls of glbChiSys to calculate the projection onto one dimension including the full n parameter correlation where Neria is the number of points in each direction of the lattice For example taking only Nia 20 and n 7 six oscillation parameters and matter density would mean more than one billion function calls of glbChiSys One can easily imagine that these would be too many for any reasonable application The solution to this problem is using a n dimensional local minimizer for the projection instead of a grid based method where we will illustrate this minimization process later It turns out that such a minimizer can include a full 6 parameter correlation with of the order of 1000 function calls of glbChiSys For the minimization we use a derivative free method due to Powell in a modified 7 version Not needing derivatives is highly desired since the event rate depends in a non linear way on the oscillation parameters thus there is no easy analytical way to obtain derivatives of the x function 28 CHAPTER 4 Calculating x projections how one can include correlations Thus for each point on the projection axis plan
115. o force it into the tested minimum In addition the number of iterations used allows an optimization of the convergence speed Note that before any minimization glbSetStartingValues and glbSetInputErrors have to be used at least once In addition note that the resulting x of glbChiTheta or glbChiDelta for the combination of more than one experiment is not equal to the sum of the individual x values anymore This has two reasons First the topology of the fit manifold is altered by the addition of x values of different experiments Thus after the minimization the position of the minimum can be different to the ones of the individual experiments Second the priors for the external knowledge on the parameters are only added once independent of the number of experiments The output of the minimizer in out carries as many matter density scaling factors as there are experiments Either one for the simulation of one experiment or all for the simulation of all experiments are different from 1 0 if matter density uncertainties are present since each experiment may face other matter density conditions The minimizers of individual experiments know which experiment they are currently treating which means that they only returned the matter density scaling factor of the appropriate experiment For example calculating glbChiTheta for the last experiment number the last density value will be returned This approach turns out to be extremely u
116. o solve this double integral numerically we split up the two integrations First we evaluate the integral over E where the only terms containing E are kIT B T E 5 and V3 E E We define Rg E E je B faf dE ki E E Ve E E 9 4 Thus Ro E E describes the energy response of the detector i e a neutrino with a true energy E is reconstructed with an energy between E and E dE with a probability Ri E E dE The function R E E is also often called energy resolution function Actually its internal representation in the software is a smearing matrix The function eg E will later be refered to as post smearing efficiencies since it will allow us to define cuts and threshold functions after the smearing is performed i e as function of F 9 4 Oscillation channels 73 The detailed definition and initialization of the energy resolution function is described in Sec 9 5 Eventually we can write down the number of events per bin 7 and channel c as E AE 2 dni ee dE E 9 5 _ 2 dE where AEF is the bin size of the ith energy bin This means that one has to solve the integral E AE 2 Fr nf N L dE fe E P E o E R E E e E 9 6 E AE 2 J Note that the events are binned according to their reconstructed energy A simple channel definition in GLoBES consists of the flux the CP sign of the ini tial state the initial flavor the fina
117. of numbers Here the lists contain only one element because we only use one density layer We initialize a baseline length of 3000 km with a constant matter density of 3 5 g cm As another ingredient we have to define the energy resolution function energy resolution energy MINOS lt type 1 sigma_e 0 15 0 0 0 0 gt The energy command starts the energy environment which has the name MINOS here Out of several possibilities it uses algorithm one the simplest and fastest one The actual energy resolution is specified by the energy resolution variable which is a list of three elements Each element is one parameter of the general resolution function as defined in Eq 9 12 Now we have all pieces to be able to define the appearance and the corresponding disappearance channel of a neutrino factory Ve V and D D u stored 8 2 A simple example for AEDL 63 channels channel appearance lt channel mu_plus electron muon CC MINOS gt channel disappearance lt channel mu_plus muon muon CC MINOS gt The first element is the name of the flux which we have defined above The second element determines whether neutrinos or anti neutrinos are taken from the flux table two different polarities allowed The third position defines the initial flavor and the forth position the final flavor followed by the name of the cross section and energy resolution function as d
118. of sampling points is smaller than the energy resolution e The edges are treated correctly e The neutrino oscillations are slow on a scale of the smapling point distance 78 CHAPTER 9 Experiment definition with AEDL In this case Eq 9 9 is reduced to nf N L amp E P E 0 E Kf E AB 9 10 j 1 The advantages of this algorithm are obvious All factors independent of the oscillation parameters have to be only evaluated once at values of which are known in advance which means that they can be put into a look up table In addition the probability has to be only evaluated at previously known values of the energy which makes it possible to compute the transition amplitudes for all channels simultaneously One assumption is that all involved factors are piece wise constant i e they hardly change within each bin This assumption seems to be very restrictive which is however not quite correct First of all if one analyzes simulated data which are simulated with the same algorithm the errors will cancel between the simulated and fitted data Second and more important this algorithm is just a very basic integration routine and converges to the true result for decreasing step size Thus if the number of sampling points is large enough this algorithm is very accurate This algorithm is selected by type 1 within the energy environment The computation of the bin kernel Kf is performed by GLoBES Thus it
119. of that work are not derived from the Program and can be reasonably considered independent and separate works in themselves then this License and its terms do not apply to those sections when you distribute them as separate works But when you distribute the same sections as part of a whole which is a work based on the Program the distribution of the whole must be on the terms of this License whose permissions for other licensees extend to the entire whole and thus to each and every part regardless of who wrote it Thus it is not the intent of this section to claim rights or contest your rights to work written entirely by you rather the intent is to exercise the right to control the distribution of derivative or collective works based on the Program In addition mere aggregation of another work not based on the Program with the Program or with a work based on the Program on a volume of a storage or distribution medium does not bring the other work under the scope of this License CHAPTER The GNU General Public License 101 3 You may copy and distribute the Program or a work based on it under Section 2 in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following a Accompany it with the complete corresponding machine readable source code which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange or
120. omputed with glbChiSys The right hand plot illustrates the projection of this two dimensional manifold onto the sin 2013 axis by minimizing x over dcp In this simple example the minimization is done along the vertical gray lines in the left hand plot The obtained minima are located on the thick gray curve which means the the right hand plot represents the x value along this curve In fact one can easily see that one obtains the correct projected 30 errors in this example cf arrows This figure illustrates the projection of a two parameter correlation In general the full n parameter correlation is treated similarly by the simultaneous local minimization over all free fit parameters 32 CHAPTER 4 Calculating y projections how one can include correlations Example Projection of two and n dimensional manifold onto sin 20 3 azris This example demonstrates how to project the fit manifold onto the sin 2013 axis i e how one can include correlations We compute two sets of data one for keeping all pa rameters but dcp fixed two parameter correlation and one for keeping all parameters free multi parameter correlation However we impose external precisions for the solar parameters and the matter density The following code excerpt is from example2 c Set starting values and input errors for all projections glbDefineParans input_errors theta12 0 1 0 0 0 sdm 0 1 0 glbSetDensityParams input_errors 0 05 GLB_ALL glbSet
121. onents are always a function of the reconstructed neutrino energy E such as the post smearing efficiencies ey E in Eq 9 4 Examples for post smearing efficiencies are cuts and detection threshold functions All post smearing components have to have as many elements as there are energy bins Efficiencies are multiplicative and their default value is 1 whereas backgrounds are additive and their default value is 0 Thus a more elaborate channel can be defined as channel channel_1 lt channel flux muon muon cross energy pre_smearing background 1 2 3 4 5 6 7 8 9 10 post_smearing_efficiencies 0 1 0 2 0 3 0 4 0 5 gt This experiment uses 10 sampling points and 5 bins In the following subsections we will define the energy resolution function All energy resolution functions are defined within an energy environment and can be refered to by name energy name lt gt The individual parameters of the environment will be defined below and depend on the algorithm used 9 5 2 Bin based automatic energy smearing This algorithm is the simplest of the built in algorithms for the evaluation of Eq 9 9 It is applicable to most of the experiments which can be simulated with GLoBES The key idea is to use a flat model i e the integrand of Eq 9 9 is well approximated by being piecewise constant in each sampling step This is a good approximation as long as e No details are lost i e the spacing
122. orithm it would then be rather difficult to converge into the unwanted true sign solution However note that one should in this case check that the actually determined value for Am3 after minimization is close enough to the guessed value Am3 in order to avoid significant artifical contribu tions of the priors to the final x Alternatively one could re run the minimizer with the position of the previously found minimum as starting position but now with switching off the constraint on Am3 In order to set the starting values and input errors two function have to be called before the usage of any minimizer Function 4 1 int glbSetStartingValues const glb_params in sets the starting val ues for all of the following minimizer calls to in Function 4 2 int glbSetInputErrors const glb_params in sets the input errors for all of the following minimizer calls to in An input error of 0 corresponds to not taking into account the respective prior Accordingly there are functions to return the actually set starting values and input errors Function 4 3 int glbGetStartingValues glb_params out writes the currently set starting values to out Function 4 4 int glbGetInputErrors glb_params out writes the currently set input errors to out All functions take or return as many matter density parameters as there are initialized experiments In addition they return 1 if the operation was not successful Eventually a typical initialization of
123. ormally provide the length of the lists N by means of an additinal argument which is a pointer to size_t Normally it is enough to declare a variable of the type size_t and to give its address to the function The following functions return matter density profiles Function 7 4 int glbLoadProfileData const char filename size_t layers double lengths double densities loads a density file from the file filename It returns the number of layers layers the list of lengths lengths and the list of densities densities The file should contain in each line a length and density for one layer which are separated by an empty space Function 7 5 int glbStaceyProfile double baseline size_t layers double lengths double densities creates a PREM Stacey matter density profile with a number of layers steps for the baseline baseline The list of lengths lengths and the list of densities densities are returned 7 1 Baseline and matter density profile 49 Function 7 6 glbAverageDensityProfile double baseline double lengths double densities creates a average matter density profile from the PREM Stacey profile with one step for the baseline baseline The list of lengths lengths and the list of densities densities are returned The average matter density p L for a matter density profile p x along the baseline L baseline is defined as L pad 0 where d is the PREM matter density as function of the distance d to the Earth s core
124. ory flux is flux mu_plus lt builtin 1 parent_energy 50 0 stored_muons 5 33e 20 time 8 0 gt For a user defined flux one has to give it the file name flux user lt flux_file user_file_i dat time 2 0 power 4 0 norm 1e 8 9 2 Baseline and matter density profile 69 In this case the norm variable is an overall normalization which defines a conversion factor from the fluxes in the file to the units in GLoBES In general there are many ways to give the source power of a neutrino source such as neutrinos per proton on target per area per time frame Right now each flux has its own normalization factor which is not always straightfoward to calculate Often one has to take into account many things such as the number of target particles per unit mass In addition the fluxes will be rescaled by 1 L which means that the normalization must contain a factor L3 Here Lo is the distance from the source for which the flux is given to the actual neutrino production region At the end it is left to the user to ensure that the numbers in the flux file give after the multiplication with norm the proper numbers of produced neutrinos corresponding to the chosen target power power Usually this adjustment of norm is performed by comparison with known energy spectra for a specific experiment The software assumes that the given flux file has seven columns and 501 lines with equidistant energies The format is
125. ose Systematics only glbChiSys x with systematics only Projections onto axes glbChiTheta Projection onto 6013 axis glbChiDelta Projection onto dcp axis glbChiTheta23 Projection onto 493 axis glbChiDm Projection onto Am3 axis glbChiDms Projection onto Am3 axis Projection onto plane glbChiThetaDelta Projection onto 013 dcp plane Projection onto any hyper plane glbChiNP Projection onto any n dimensional hyper plane Localization of degeneracies CHAPTER 1 A GLoBES tour Parameters Result glb_params in int exp int rule double x glb_params in glb_params out int exp double x glb_params in glb_params int exp double x out glb_params in glb_params out int exp double x glb_params in glb_params int exp double x out glb_params in glb_params out int exp double x glb_params in glb_params int exp double x out glb_params in glb_params out int exp double x Needs glbSetProjection before glbChiAll Local Minimization glb_params in glb_params out over all parameters int exp double y Table 1 1 The GLoBES standard function to obtain a x value with systematics only or systematics and correlations The parameters rule and exp can either be GLB_ALL for all initialized experiment or the experiment number 0 to glb_num_of_exps 1 for a specific experiment The format of glb_parans is discussed in detail in
126. ot possible to produce a too pessimistic solution However if one is not careful enough to locate all local minima one can easily produce too optimistic solutions This danger can be summarized as follows Too pessimistic result lt Real result lt GLoBES result lt Too optimisitic result Located by careful usage NB Implementing a grid based method which guarantee to find all local minima is not straightforward either to say the least 4 2 The treatment of external input 29 In many cases the fit manifold is restricted by the knowledge from earlier experiments For example the knowledge on the solar parameters will in most cases be supplied by the solar neutrino experiments If the external precision of a parameter is at the time of the measurement better than the one of the experiment itself one usually will use this external better knowledge and impose a corresponding constraint on this parameter This external knowledge may reduce the extension of the n dimensional fit manifold in the respective direction In the most extreme case keeping all parameters but the measured one fixed in the analysis is equivalent to the assumption that all parameters are determined externally with infinitively high precisions As this is a quite strong assumption one should always check the consequences of relaxing it and using realistic errors Only if such a test has demonstrated that the impact of the uncertainty on a given fit parameter is negligib
127. p int fluxno returns the source power of experiment number exp and flux number fluxno Function 2 6 void glbSetRunningTime double time int exp int fluxno sets the running time of experiment number exp and flux number fluxno to time years Function 2 7 double glbGetRunningTime int exp int fluxno returns the running time of experiment number exp and flux number fluxno Function 2 8 void glbSetTargetMass double mass int exp sets the fiducial detec tor mass of experiment number exp to mass tons or kilotons depending on the experiment definition Function 2 9 double glbGetTargetMass int exp returns the fiducial detector mass of experiment number exp Thus these functions also demonstrate how to use the assigned experiment number and others These numbers run from 0 to the number of experiments 1 fluxes 1 etc where the individual elements are numbered in the order of their appearance Note that the source power and running time are quantities defined together with the neutrino flux whereas the target mass scales the whole experiment Thus if one has for instance a neutrino and an antineutrino running mode one can scale them independently 2 3 Handling oscillation parameter vectors 19 2 3 Handling oscillation parameter vectors Before we can set the simulated event rates or access any oscillation parameters we need to become familiar with the concept GLoBES uses for oscillation parameters In order to transfer sets of oscil
128. parameters other than dcp and the fixed fit value of dcp The actually determined parameters at the minimum are returned in out where dcp is still at its fixed value If out is set to NULL this information will not be returned All of the minimization functions have a similar parameter structure The fixed fit parameter value and the guessed starting point of the minimizer i e the guessed position of the minimum are transferred in the list in Part of this list are the matter density scaling factors of all experiments which are also minimized over The minimizer is then 34 CHAPTER 4 Calculating y projections how one can include correlations started at the guessed point and runs into the local minimum where the fit parameter of the projection axis is fixed For the true solution it is usually sufficient to start the minimizer at the true parameter values However the convergence speed might be better by starting it slightly off this point In addition there are problems in many cases with more complicated topologies which means that better guesses for the position of the minimum are needed The position of the minimum is then returned in out together with the number of iterations used for the minimization It is very often useful to print the output of the minimization with glbPrintParams in order to check that the minimum is the appropriate one For example if the minimizer ends up in the wrong sign solution in Am3 priors can be used t
129. pendix 10 2 and the INSTALL file in the software package We demonstrate how to load pre defined experiments and introduce the basic concepts of GLoBES We do not go into details of the programming language which means that standard parts of the program code common to all of the examples in the following chapters are in general omitted An example of a minimal GLoBES program in C can be found on page 14 Furthermore the files of the examples in this part can be found in the example subdirectory of your GLoBES distribution After the installation of GLoBES they can be compiled using the Makefile in the examples directory The Makefile has been correctly setup by the configure script to take into account details of the installation on your system Thus you ve just to type make and you re done This Makefile very well serves as a template for your own applications We will in this part not go into details of the experiment definition The pre defined experiment prototypes in the data subdirectory are summarized in Table 2 1 They cor respond except from minor modifications to the experiments in the respective references in the table These files are installed to the directory prefix share globes which usually defaults to usr local share globes It is useful to add this path to the value of GLB_PATH 2 1 Initialization of GLoBES Before one can use GLoBES one has to initialize the GLoBES library Function 2 1 void glbInit char name i
130. plified version of a neutrino factory experiment It still lacks the correct energy dependence of the efficiencies the antineutrino disappearance channel and the channels and rules for the symmetric operation with u stored However it may serve as a simple introductory example In the next chapter we will demonstrate that the AEDL is much more powerful than illustrated here 64 CHAPTER 8 Getting started 8 3 Introduction to the syntax of AEDL We now give a short introduction to the syntax of AEDL The first eight characters have to be GLoBES in order to avoid parsing megabytes of chunk and producing thousands of error messages Comments can be used such as in C This starts a comment and here the comment ends There are pre defined variables which all start with Their range is also checked For example bins can be only between 0 and 500 If one uses a float quantity where an int is expected the float will be converted to an int in the same way as in C For example we have scalar variables bins 10 baseline 1200 0 and simple lists densitytab 1 0 2 2343 3 3432 Since there are often groups of data which we want to refer to later environments can be used This is illustrated with the channel definition part channel ch1 lt gt The first part is the type of environment which is channel here There are the following types of environment in AEDL flux cross channel energy rule Besides the en
131. r all defined oscillation channels for an experiment or any combination of experiments Of course also low level information such as oscillation probabilities or event rates can be obtained GLoBES includes the simulation of neutrino oscillations in matter with arbitrary matter density profiles as well as it allows to simulate the matter density uncertainty As one of the most advanced features of GLoBES it provides the technology to project the Ay which is a function of all oscillation parameters onto any subspace of parameters by local minimization This approach allows the inclusion of multi parameter correlations where external input e g from solar parameters can be imposed too Applications of the projection mechanism include the projections onto the sin 26 3 axis and the sin 20 3 dcp plane In addition all oscillation parameters can be kept free to precisely localize degenerate solutions II III Terms of usage of GLoBES Referencing the GLoBES software GLoBES is developed for academic use Thus the GLOBES Team would appreciate being given academic credit for it Whenever you use GLoBES to produce a publication or a talk indicate that you have used GLoBES and please cite the reference 1 P Huber M Lindner and W Winter Simulation of long baseline neutrino oscillation experiments with GLoBES arXiv hep ph 0407333 but not this manual This manual itself is not a scientific publication and will not be submitted to a s
132. requires that the number of bins bins and the minimum energy emin and maximum energy emax are given in case of equidistant bins As far as the parameterization for the energy resolution function R E E in Eq 9 8 is concerned the algorithm uses a Gau ian RE BE ee 9 11 5 e o a o E v2r There are several energy resolution functions available where by default standard is used sigma_function standard The energy resolution function standard is defined by o E a E VE Y 9 12 where the parameters a 8 and y are provided by the user sigma_e 0 15 0 0 0 0 5It is planed for to have something like a Gau8 Kronrod scheme as an alternative here 9 5 Energy resolution function 79 Currently another possible choice for sigma_function is inverse_beta which only uses the parameter a It is defined by 1 8 70 810 3 oE v1000 VWz 8 10 4 forx gt 1 8 10 0 13 a 10 3 for z lt 1 8 1073 The somewhat complicated form is due to the fact that inverse decay has a neutrino threshold of 1 8 MeV and that a neutrino at threshold already produces 1 MeV visible energy in the detector for more details see e g 6 In the actual implementation of the algorithm the sum in Eq 9 10 is only computed for the E s where K E is above a certain threshold which is by default 10 This threshold is defined at the compiling time Eventually a complete energy resolution definition of this
133. restrictions translate to certain responsibilities for you if you distribute copies of the software or if you modify it For example if you distribute copies of such a program whether gratis or for a fee you must give the recipients all the rights that you have You must make sure that they too receive or can get the source code And you must show them these terms so they know their rights We protect your rights with two steps 1 copyright the software and 2 offer you this license which gives you legal permission to copy distribute and or modify the software Also for each author s protection and ours we want to make certain that everyone understands that there is no warranty for this free software If the software is modified by someone else and passed on we want its recipients to know that what they have is not the original so that any problems introduced by others will not reflect on the original authors reputations Finally any free program is threatened constantly by software patents We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses in effect making the program proprietary To prevent this we have made it clear that any patent must be licensed for everyone s free use or not licensed at all The precise terms and conditions for copying distribution and modification follow TERMS AND CONDITIONS FOR COPYING DISTRIBUTION AND MODIFICATION 100 CHAPTER The GNU G
134. rivatives Prentice Hall 1973 T Ohlsson and H Snellman Neutrino oscillations with three flavors in matter Applications to neutrinos traversing the earth Phys Lett B474 2000 153 162 hep ph 9912295 Erratum ibidem B480 419 E 2000 T Ohlsson and W Winter The role of matter density uncertainties in the anal ysis of future neutrino factory experiments Phys Rev D68 2003 073007 hep ph 0307178 K Kiers S Nussinov and N Weiss Coherence effects in neutrino oscillations Phys Rev D53 1996 537 547 hep ph 9506271 C Giunti Coherence and wave packets in neutrino oscillations Found Phys Lett 17 2004 103 124 hep ph 0302026 G L Fogli E Lisi A Marrone D Montanino and A Palazzo Getting the most from the statistical analysis of solar neutrino oscillations Phys Rev D66 2002 053010 hep ph 0206162 112 BIBLIOGRAPHY Indices 113 114 API functions _exp 17 _experiment_list 16 _hum_of_exps 4 16 _params 4 17 19 23 _projection 17 35 36 AllocParams 20 AllocProjection 36 AverageDensityProfile 49 ChiAll 4 39 40 ChiDelta 4 33 ChiDm 4 35 ChiDms 4 35 ChiNP 4 31 34 36 ChiSys 4 23 24 ChiTheta 4 33 ChiTheta23 4 35 ChiThetaDelta 4 35 ClearAEDLVariables 53 ClearExperimentList 17 CopyParams 20 CopyProjection 36 DefineAEDLVariable 52 DefineParams 20 DefineProjection 36 Flux 46 FreeProjection 36 GetBaselineInExperiment 48 GetBGCen
135. rplane 35 the minimizer jumps from one minimum to another In such cases the starting point of the minimizer has to be adjusted to help it find the true minimum Other examples for projections onto a parameter axis while keeping exactly one param eter fixed are glbChiTheta23 glbChiDm and glbChiDms which can be found in Table 1 1 on page 4 4 4 Projection onto any hyperplane In general one can show the measurement result in any k dimensional hyperplane where k is smaller than the dimension of the parameter space n and thus the dimension of the fit manifold In this case k parameters are fixed and n k parameters are minimized over One such example is the projection of the fit manifold onto the sin 263 dcp plane ie k 2 here In this case the two parameters sin 20 3 and dcp are kept fixed and the others are minimized over The corresponding function is Function 4 7 double glbChiThetaDelta const glb_params in glb_params out int exp returns the projected x onto the 613 dcp plane for the experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all parameters other than 013 and dcp and the fixed fit values of 013 and dcp The actually determined parameters at the minimum are returned in out where 613 and dcp are still at their fixed values If out is set to NULL this information will not be returned This function works analogously
136. seful together with the simulation of more than one experiment One can for instance locate the degeneracies of all individual experiments In order to test if these degeneracies are still present in the combination of all experiments which has a very different topology one can test the combination of experiments with the output out from the individual experiments In this case even the correct matter density scaling factor output is used The example on page 32 demonstrates how one can obtain Fig 4 1 right with keeping all parameters but dcp fixed as well as how one can include the full n parameter correlation with external input It also demonstrates how these two compare to each other One can easily read off this example that there is a substantial impact of the correlation with oscillation parameters other than dcp Note that it uses the function glbChiNP for arbitrary projections from the next section for the minimization over dcp In addition there is one interesting feature in guessing the oscillation parameters in this example In order to avoid falling into the wrong minimum the fit value of dcp is guessed from Fig 4 1 left This quite sophisticated guessing is typical for neutrino factories because of the dcp 413 degeneracy whereas it is for superbeams often sufficient to use the true values A strong indication for a wrong guessing are discontinuous jumps in the projected x function where 4 4 Projection onto any hype
137. stematical error It is based upon replacing the events in the ith bin by the ones at the energy 1 b Ei If this target energy does not exactly hit a discrete bin energy Ex linear interpolation is used We use the following approximation si a b 1b sk 1 a sk a 6 k se a 9 27 2 biG ENE k div 1 Here AF is the bin width emax emin bins and div refers to the integer part of the division Note that the factor 1 b in the first equation comes from a renormalization of the bin width since also the bin width is altered by the replacement of the energies Furthermore special care has to be payed to the limits k lt 1 or k 1 gt Npins since there Sk Or Sp41 May not have been calculated By default it is assumed that s is zero in those cases However if the event rates are still large at the limits errors will be introduced leading to a wrong estimate of the impact of the calibration error In this case one should truncate the analysis range by a few bins at the boundaries and therefore ensure in this way that only those s are used whose index k is within the range 0 Nbins 1 cf Fig 9 1 Thus it is possible to constrain the analysis energy range with each rule to an energy window energy_window 4 0 50 0 The default energy window is given between the minimal and maximal reconstructed en ergy To be on the save side reduce analysis window compared to the bin range on each si
138. t A specific experiment exp and a specific rule rule have to be chosen as well as the signal or background rate signal either GLB_SIG or GLB_BG The position pos refers to the component within the signal or background and can also be GLB_ALL The function may return the rates with GLB_W_COEFF or without GLB_WO_COEFF overall efficiency coefficient as it is specified by coeffi In addition it may contain the post smearing efficiencies set effi to GLB_W_EFF or GLB_WO_EFF and the post smearing backgrounds set bgi to GLB_W_BG or GLB_WO_BG The pre smearing efficiencies and backgrounds cannot be accessed at the rule level The return value is 0 if successful and 1 if unsuccessful Function 6 6 double glbTotalRuleRate int exp int rule int pos int effi int bgi int coeffi int signal returns the total rates with the same parameters as glbShowRuleRates The function glbTotalRuleRate is especially useful if one wants to draw bi rate graphs with total event rates or look for the dcp 13 degeneracy by the intersection of neutrino and antineutrino constant event rate curves In order to obtain information on the structure of the rules a number of additional functions are provided Function 6 7 int glbGetNumberOfRules int exp returns the number of rules in ex periment exp Function 6 8 int glbGetLengthOfRule int exp int rule int signal returns the length of rule rule in experiment exp The parameter signal can be either GLB_SIG
139. t int exp int on_off sets the filter state in experiment exp to on GLB_ON or off GLB_OFF Function 7 23 int glbGetFilterStateInExperiment int exp returns the filter state of experiment exp Analogously the filter value can be accessed Function 7 24 int glbSetFilter double filter sets the currently used filter to the value filter Function 7 25 double glbGetFilter returns the currently used filter value 54 CHAPTER 7 Changing experiment parameters at running time Function 7 26 int glbSetFilterInExperiment int exp double filter sets the filter in experiment exp to the value value Function 7 27 double glbGetFilterInExperiment int exp returns the filter value of experiment exp The return value of all Set functions is 1 if they were not successful Part Il The Abstract Experiment Definition Language AEDL 57 Chapter 8 Getting started Here the general concept of the AEDL is described and illustrated by an example In addition a short introduction to the syntax of the AEDL is given 8 1 General concept of the experiment simulation The goal of AEDL is to describe a large number of complex and very different experiments by a limited number of parameters It allows a representation of very different setups within one data structure and thus implements universal rate and x computation methods For experiment simulations usually a new piece of code is written and compiled for each different exp
140. t s22thetal3 is unchanged kept fixed Ag n n pow sin 2 glbGetOscParams minimum GLB_THETA_13 2 Output chi2 with correlations 2 1038 Position of minimum thetal2 thetal3 theta23 delta sdm ldm rho 0 542002 0 0193698 0 747915 1 77688 6 66156e 05 0 00200817 1 00434 Iterations 1693 Note that s22thetal3 is unchanged kept fixed 0 0015 Instead of including the full correlation we can take the correlation with every parameter except from dcp i e we keep in addition to 013 dcp fixed This corresponds to projection onto the sin 2013 cp plane chi2 glbChiThetaDelta fit_values minimum GLB_ALL fprintf stream chi2 with correlations other than with deltacp 4g n n ch12 CHAPTER 1 A GLoBES tour 7 Output chi2 with correlations other than with deltacp 4 32831 Similarly we can only take into account the correlation with dcp For this we need to define our own user defined projection where only dcp is a free parameter glb_projection myprojection glbAllocProjection glbDefineProjection myprojection GLB_FIXED GLB_FIXED GLB_FIXED GLB_FREE GLB_FIXED GLB_FIXED glbSetProjection myprojection chi2 glbChiNP fit_values minimum GLB_ALL fprintf stream chi2 with correlation only with deltacp Ag n n chi2 glbFreeProjection myprojection Output chi2 with correlation only with deltacp 2 80651 We can also switch of the systematics and compute the statistics x only glbSwitchS
141. tall 9 The default install directory prefix is usr local Consult the Further Information section below for instructions on installing the library in another location or changing other default compilation options The install target also will install a program with name globes to prefix bin and the files in the data directory of the tar ball to prefix share globes If you are not using make install you will find the static libary at source lib libglobes a which you can copy to any destination However keep in mind that the linking command will be somewhat different i e you have to specify all the dynamically linked objects besides libglobes which are lm lgsl lgslcblas 1f2c llapack lblas In general it is advisable to use the shared libraries If you don t have root privileges see the corresponding section page 95 If you install GLoBES with root privileges do not forget to run ldconfig after installation Basic Installation The configure shell script attempts to guess correct values for various system dependent variables used during compilation It uses these values to create a Makefile in each directory of the package Finally it creates a shell script config status that you can run in the future to recreate the current configuration a file config cache that saves the results of its tests to speed up reconfiguring and a file config log containing compiler output useful mainly for debugging configure If you ne
142. ters 52 GetBGErrors 52 GetChannelInRule 45 GetChannelRates 45 GetCoefficientInRule 45 GetDensityParams 21 GetDensityProjectionFlag 36 GetErrorDim 50 GetFilter 53 CHAPTER Indices GetFilterInExperiment 54 GetFilterState 53 GetFilterStateInExperiment 53 GetInputErrors 30 GetIteration 21 GetLengthOfRule 44 GetNormalizationInRule 45 GetNumberOfChannels 46 GetNumberOfRules 44 GetOscillationParameters 22 GetOscParams 20 GetProfileDataInExperiment 49 GetProfileType 47 GetProjection 36 GetProjectionFlag 36 GetRunningTime 18 GetSignalErrors 52 GetSourcePower 18 GetStartingValues 30 GetTargetMass 18 GetUserData 45 Init 13 InitExperiment 15 16 52 65 LoadProfileData 48 NameToValue 43 65 PrintParams 20 34 PrintProjection 36 ProfileProbability 43 ResetRateStack 46 SetBaselineInExperiment 47 SetBGCenters 52 SetBGErrors 52 SetDensityParams 20 SetDensityProjectionFlag 36 SetErrorDim 50 SetFilter 53 API FUNCTIONS SetFilterInExperiment 54 SetFilterState 53 SetFilterStateInExperiment 53 SetInputErrors 4 30 34 SetIteration 21 SetNewRates 73 SetOscillationParameters 21 22 SetOscParams 20 SetProfileDataInExperiment 49 SetProjection 4 36 SetProjectionFlag 36 SetRates 21 22 73 SetRunningTime 18 SetSignalErrors 50 SetSourcePower 18 SetStartingValues 4 30 34 SetTargetMass 18 ShowChannelRates 45 ShowRuleRates 44 StaceyProfile 48 SwitchSyste
143. the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement State on the Title page the name of the publisher of the Modified Version as the publisher Preserve all the copyright notices of the Document Add an appropriate copyright notice for your modifications adjacent to the other copyright notices Amo Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under the terms of this License in the form shown in the Addendum below Q Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice H Include an unaltered copy of this License I Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publisher of the Modified Version as given on the Title Page If there is no section Entitled History in the Document create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence 108 CHAPTER GNU Free Documentation License J Preserve the network
144. the actual matter density profile such as given by the experiment definition file and g to the relative matter density uncertainty e g 0 05 for 5 uncertainty In principle one can set the priors for the matter density and all oscillation parameters For example if the disappearance channels of the experiment determine the leading oscil lation parameters with unprecedented precisions one can omit the respective input errors In GLoBES a value of 0 corresponds to neglecting the prior If however earlier external 3to be precise a value for the error in between 10 and 107 30 CHAPTER 4 Calculating x projections how one can include correlations measurements provide better information one can set their absolute precisions with the input errors The starting values are usually chosen to be the best fit values of this exter nal experiments such as for the input from solar experiments In some cases it may be necessary to adjust them such as for artificial constraints to the oscillation parameters In other cases minor modifications of the starting values can cause a faster convergence of the algorithm For example for the investigation of the opposite sign solution one can use the prior to constrain Am3 in order to force the minimizer not to fall into the unwanted true sign solution In this case the starting value of Am3 would be set to Pam Ami3 and a 0 3 of the order of Am3 would be imposed For the alg
145. the text A section Entitled XYZ means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a section Entitled XYZ according to this definition The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License 2 VERBATIM COPYING You may copy and distribute the Document in any medium either commercially or noncommercially provided that this License the copyright notices and the license notice saying this License applies to the Document are reproduced in all copies and that you add no other conditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you distribute a large enough number of copies you must also follow the
146. the value of the density parameter which in the structure in Function 2 19 glb_params glbSetIteration glb_params in int iter sets the number of iterations in the structure in to the value iter If the assignment was unsuccessful the function returns NULL Function 2 20 int glbGetIteration glb_params in returns the value of the number of iterations in the structure in In total the parameter vector handling in a program normally has the following order glbInitExperiment more initializations glb_params vectori glbAllocParams more vectors allocated Program code assign and use vectors glbFreeParams vector1 more vectors freed end of program or glbClearExperimentList 2 4 Computing the simulated data Compared to existing experiments which use real data future experiments use simulated data Thus the true parameter values and their results in form of the reference event rate vectors are simulated After setting the true parameter values the fit parameter values can be varied in order to obtain information on the measurement performance for the given set of true parameter values Therefore it is often useful to show the results of a future measurement as function of the true parameter values for which the reference rate vectors are computed at least within the currently allowed ranges The true parame ter values for the vacuum neutrino oscillation p
147. these Invariant Sections You may include a translation of this License and all the license notices in the Document and any Warranty Disclaimers provided that you also include the original English version of this License and the original versions of those notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer the original version will prevail If a section in the Document is Entitled Acknowledgements Dedications or History the require ment section 4 to Preserve its Title section 1 will typically require changing the actual title 9 TERMINATION You may not copy modify sublicense or distribute the Document except as expressly provided for under this License Any other attempt to copy modify sublicense or distribute the Document is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such parties remain in full compliance 10 FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new revised versions of the GNU Free Documentation License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft Each version of the License is given a disti
148. third parties to this License 7 If as a consequence of a court judgment or allegation of patent infringement or for any other reason not limited to patent issues conditions are imposed on you whether by court order agreement or otherwise that contradict the conditions of this License they do not excuse you from the conditions of this License If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations then as a consequence you may not distribute the Program at all For example if a patent license would not permit royalty free redistribution of the 102 10 11 12 CHAPTER The GNU General Public License Program by all those who receive copies directly or indirectly through you then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program If any portion of this section is held invalid or unenforceable under any particular circumstance the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims this section has the sole purpose of protecting the integrity of the free software distribution system which is implemented by public license practices Many people have made generous contributions to
149. tion errors These errors are assumed to be independent between the signal events and the 6In fact the pull method was employed already in Ref 5 before Ref 12 appeared 9 6 Rules and the treatment of systematics 83 background events which means that this systematics treatment defines the grouping into signal or background The implementation of the normalization error is straightforward sila a si 9 25 with an analogous definition for the background events Here a is the nuisance parameter which will be minimized over later For the parameterization of an energy calibration error two possibilities are imple mented The first one method T is somewhat simpler whereas the second one method C is more accurate but it requires a careful choice of parameters The first option method T is sila b sila b s Ei Eux E max miah 9 26 where E n and E ax correspond to emin and emax and E is the mean reconstructed energy of the ith bin It is often refered to as a tilt of the spectrum since it describes a linear distortion of the event rate spectrum Note that this definition of a tilt makes only sense in combination with a large enough normalization error since the tilt also affects the normalization The second option method C is closer to an actual energy calibration error which means that one should test this option whenever one suspects a large impact of this sy
150. tion region such as in the sun or in reactor experiments with many neutrino sources e g KamLAND Therefore a neutrino source in GLoBES can in general be characterized by the flux spectrum for each neutrino flavor the CP sign neutrinos or antineutrinos and the total luminosity of the source Before we come to the definition of the source properties let us discuss the total inte grated luminosity of the experiment In GLoBES the total number of events is in general proportional to the product of Source power MW GW Useful muon decays yr 2 1 Fid detector mass kt t x Running time yr x Thus the source power corresponds to either the amount of energy produced per time frame in the target such as for nuclear reactors or sources based on pion decay or the useful muon decays per time frame neutrino factories In addition the definition of the source power makes only sense together with the flux normalization the running time and fiducial detector mass in order to define the total integrated luminosity Therefore one can in principle use arbitrary units for these components as long as their product gives the wanted neutrino flux However it is recommended to use normalizations such that the source power units are MW for a proton based beam and GW tnermal for a reactor 68 CHAPTER 9 Experiment definition with AEDL experiment Correspondingly the detector mass units should be kilotons for a proton based beam
151. to download using public standard network protocols a complete Transparent copy of the Document free of added material If you use the latter option you must take reasonably prudent steps when you begin distribution of Opaque copies in quantity to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy directly or through your agents or retailers of that edition to the public It is requested but not required that you contact the authors of the Document well before redis tributing any large number of copies to give them a chance to provide you with an updated version of the Document 4 MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use in the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission B List on
152. tor if successful or they are NULL if unsuccessful the 013 axis glbChiTheta is nothing else than a special case of glbChiNP with 913 fixed and all the other parameters free Similar to glb_params the type glb_projection has to be allocated first and freed later The access functions for glb_projection are summarized in Table 4 1 Since the complete set is very similar to the one for glb_params we do not go into greater details here As soon as we have defined a projection we can assign it Function 4 8 int glbSetProjection const glb_projection in sets the projection to in The return value is 0 if successful and 1 if unsuccessful Similarly the currently assigned projection can be returned with Function 4 9 int glbGetProjection glb_projection out writes the currently set projection to out The return value is 0 if successful and 1 if unsuccessful After setting the starting values input errors and the projection we can run the minimizer Function 4 10 double glbChiNP const glb_params in glb_params out int exp returns the projected x onto the hyperplane specified by glbSetProjection for the 4 4 Projection onto any hyperplane 37 experiment exp For the simulation of all initialized experiments use GLB_ALL for exp The values in in are the guessed fit values for the minimizer all free parameters and the fit values on the hyperplane all fixed parameters The actually determined parameters at the minimum are returne
153. ts license notice and that you preserve all their Warranty Disclaimers The combined work need only contain one copy of this License and multiple identical Invariant Sections may be replaced with a single copy If there are multiple Invariant Sections with the same name but different contents make the title of each such section unique by adding at the end of it in parentheses the name of the original author or publisher of that section if known or else a unique number Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work In the combination you must combine any sections Entitled History in the various original docu ments forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sections Entitled Dedications You must delete all sections Entitled Endorsements 6 COLLECTIONS OF DOCUMENTS CHAPTER GNU Free Documentation License 109 You may make a collection consisting of the Document and other documents released under this License and replace the individual copies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individually under this License provided you ins
154. ture Installation Names By default make install will install the package s files in usr local bin usr local include etc You can specify an installation prefix other than usr local by giving configure the option prefix PATH CHAPTER GLoBES installation 97 Specifying the System Type There may be some features configure can not figure out automatically but needs to determine by the type of host the package will run on Usually configure can figure that out but if it prints a message saying it can not guess the host type give it the host TYPE option TYPE can either be a short name for the system type such as sun4 or a canonical name with three fields CPU COMPANY SYSTEM See the file config sub for the possible values of each field If you are building compiler tools for cross compiling you can also use the target TYPE option to select the type of system they will produce code for and the build TYPE option to select the type of system on which you are compiling the package Sharing Defaults If you want to set default values for configure scripts to share you can create a site shell script called config site that gives default values for variables like CC cache_file and prefix configure looks for PREFIX share config site if it exists then PREFIX etc config site if it exists Or you can set the CONFIG_SITE environment variable to the location of the site script A warning not all configure scripts look for
155. urrently GLoBES does not support lepton number violating transitions i e no transitions from neutrino to antineutrino or vice versa are considered 12 CHAPTER 9 Experiment definition with AEDL The differential event rate for each channel is given by na N fapa PaE x 0 0 ee 1 Ta Peo E L p 023 012 013 Ami Amd dcp x a Propagation or E ky E x ee Interaction T E V E E 9 3 S m Detection where a is the initial flavor of the neutrino is the final flavor a E is the flux of the initial flavor at the source L is the baseline length N is a normalization factor and p is the matter density The energies in this formula are given as follows e E is the incident neutrino energy i e the actual energy of the incoming neutrino which is not directly accessible to the experiment e is the energy of the secondary particle e E is the reconstructed neutrino energy i e the measured neutrino energy as ob tained from the experiment The interaction term is composed of two factors which are the total cross section ol E for the flavor f and the interaction type IT and the energy distribution of the secondary particle ki E The detector properties are modeled by the threshold function T s E coming from the the limited resolution or the cuts in the analysis and the energy resolution function Va E E of the secondary particle Since it is a lot of effort t
156. use the built in source flux for a neutrino factory originating from stored u s This achieved by setting the builtin variable to 1 Next we specify the muon energy to be 50 GeV by the parent_energy variable We assume that there will be 5 33 107 useful muon decays per year and that this luminosity is available for 8 years i e a total number of 4 264 10 muons is stored beam flux mu_plus lt builtin 1 parent_energy 50 0 stored_muons 5 33e 20 time 8 0 62 CHAPTER 8 Getting started Note that we tell GLOBES that we want to refer to this neutrino source later as as mu_plus Let us now define a very simple detector with a target mass of 50kt and 20 energy bins between 4GeV and 50 GeV target_mass 50 bins 20 emin 4 0 emax 50 0 Then we specify the file which contains the cross sections we want to use cross section cross CC lt cross_file XCC dat gt The command cross tells the parser that a cross section environment begins It has the name CC which can later be used to refer to this specific environment and thus to the file XCC dat Note that each name begins with a leading Of course the baseline and matter profile have to be specified too where we use an arbitrary matter density profile here baseline profiletype 3 densitytab 3 5 lengthtab 3000 0 The curly brackets used for the definition of densitytab and lengthtab refer to a list
157. use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall subject or to related matters and contains nothing t
158. vironment type there is a user defined name beginning with in the above example ch1 It can be used later to refer to the channel defined in lt gt Those names are so called automatic variables and have to start with Note that these names have to be unique and can only be refered to after their definition However similar to C one can give a declaration without definition before channel ch2 lt gt The upper limit is only there for safety reasons the memory is allocated dynamically 8 3 Introduction to the syntax of AEDL 65 Now one can refer to the name ch2 while the actual channel definition comes later The internal representation of this automatic variable is a number which obtains its value from a counter for each type of environment For example for channel the counter is numofchannels The counter keeps track of how many different names there are for one type of environment which means that it counts the number of channels rules energy resolution functions etc Thus the automatic variables are numbered in the order of their definition and the number can later be used to refer to them in the C code from 0 to numof 1 In order to facilitate the the mapping from names in AEDL to indices in C there are two functions glbNameToValue and glbValueToName which make this transition see Sec 6 2 page 43 Within each environment type there are several variables beginning with which can only be used wit
159. wo setting are useful to clarify path resolution issues and shadowing of file names 10 2 Testing AEDL files In the process of defining a new experiment the default output of globes at rule level is the final step However in order to arrive at this level it is often necessary to review the intermediate steps in the event rate calculation The globes utility offers many possibilities to do this based on the rate access functions as described in Sec 6 3 By default globes returns total rates corresponding to the t option This can be changed to to a full spectrum by using s The spectral rates are shown in a table where the first column always gives the central energy of the corresponding bin or the sampling point If there is more than one experiment in a file e there is at least one NEXT command only the event rates for one experiment will be shown This experiment can be chosen with the e option which takes as a mandatory argument the number of the experiment starting with zero The default is e0 Channel level As a first step one may want to check if each channel produces the anticipated output Channel rates are returned if the c option is used This option takes as an optional 10 2 Testing AEDL files 89 argument the channel number starting at zero If no argument is given all channels are displayed By default the sum of the event rates in each channel is shown Each column has as first line the same channel name
160. xps and all rules glbSwitchSystematics GLB_ALL GLB_ALL GLB_ON return res The complete code can be found as example4 c with the software which consists of many of the applications from the earlier examples In addition it uses a little trick It avoids falling into the wrong solution with glbChiTheta by using the fit value of dcp from the step before as prediction of the position of the current calculation The returned lists of data from the example represent x as function of the fit value of sin 26 3 The intersections of these curves with the line x 9 give the sin 2013 sensitivity limits at the 30 confidence level where we do not include the sgn Am and dcp 013 degeneracies in the sensitivity limit with correlations only green bar sin 20 3 senstivity limit 30 for NuFact II Systematics Correlations egeneracy 10 10 10 107 10 10 CHOOZ excluded 52 CHAPTER 7 Changing experiment parameters at running time Function 7 13 int glbGetSignalErrors int exp int rule double norm double tilt writes the signal errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 14 int glbSetBGErrors int exp int rule double norm double tilt sets the background errors of experiment exp and rule rule to norm normalization error and tilt tilt calibration error Function 7 15 int glbGetBGErrors int exp int rul
161. y one signal channel and to assign all sorts of perturbations to the background Similarly the background event rate b in the ith bin can be composed out of one or more channels bi Bey Bey 1 9 22 82 CHAPTER 9 Experiment definition with AEDL where the channels can be any combination of the ones in the signal rate and additional ones The background normalization factors very often have a specific meaning For example they may correspond to a fraction of mis identified events charge or flavor mis identification These basic building blocks of each rule are within the rule environment for example defined by channel_1 signal 0 001 channel_2 0 005 channel_3 0 5 background For the analysis of the systematical errors the so called pull method is used 12 For the pull method k systematical errors are included by introducing k additional variables Ck which are the so called nuisance parameters The nuisance parameters describe the dependence of the event rates on the various sources of systematical errors such as an error on the total normalization is included by multiplying the expected number of events in each bin by a factor 1 The variation of is in the fit constrained by adding a penalty p to the y function In case of a Gau ian distributed systematical error this penalty is given by 012 p EL 0 23 OG where denotes the mean and o the standard deviation of the
162. yntax That is the only way in which the examples deviate form ISO C Moreover the actual numerical values of the results of the examples may be different from the ones in this manual Part I User s manual Chapter 1 A GLoBES tour In this first chapter we show a GLoBES tour illustrating the main features of GLoBES The complete example can be found as example tour c in the example subdirectory of your GLoBES distribution The output is written to stream which can be either stdout or a file Details about how to use GLoBES with C can found in Chapter 2 and the following chapters You can also find a summary of the most important GLoBES y functions in Table 1 1 Note that this chapter can be skipped without loss of relevant information Initialize the GLoBES library glbInit argv 0 Define my standard oscillation parameters double thetal2 asin sqrt 0 8 2 double theta13 asin sqrt 0 001 2 double theta23 double deltacp double sdm M_PI 4 M_PI 2 Te 5 double ldm 2e 3 Load one neutrino factory experiment glbInitExperiment NuFact glb amp glb_experiment_list 0 amp glb_num_of_exps Initialize a number of parameter vectors we are going to use later glb_params glb_params glb_params glb_params glb_params true_values glbAllocParams fit_values glbAllocParams starting values glbAllocParams input_errors glbAllocParams minimum glbAllocParams Function Purp
163. ystematics GLB_ALL GLB_ALL GLB_OFF chi2 glbChiSys fit_values GLB_ALL GLB_ALL glbSwitchSystematics GLB_ALL GLB_ALL GLB_ON fprintf stream chi2 with statistics only wg n n chi2 Output chi2 with statistics only 39 143 Let us now locate the exact position of the sgn degeneracy glbDefineParams input_errors theta12 0 1 0 0 0 sdm 0 1 1dm 3 glbDefineParams starting _values theta12 theta13 theta23 deltacp sdm ldm glbSetDensityParams input_errors 0 05 GLB_ALL glbSetStartingValues starting_values glbSetInputErrors input_errors chi2 glbChiAll starting_values minimum GLB_ALL fprintf stream chi2 at minimum g n chi2 fprintf stream Position of minimum thetal2 thetal3 theta23 delta sdm ldm rho n glbPrintParams stream minimum For a exact definition of inverted hierarchy see page 19 8 CHAPTER 1 A GLoBES tour Output chi2 at minimum 6 20025 Position of minimum thetal2 thetal3 theta23 delta sdm Idm rho 0 591812 0 0264717 0 72763 1 08709 8 0004e 05 0 00206094 0 970685 Iterations 1946 After testing these functions with only one experiment let us now go to a two experiment setup with two different neutrino factory baselines Since the GLoBES parameter vectors depend on the number of experiments we have to free them first glbFreeParams true_values glbFreeParams fit_values glbFreeParams starting values glbFreeParams input_errors glbFreeParams min

GLoBES GLoBES

Contents

Download Pdf Manuals

Related Search

Related Contents