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The micrOMEGAs user`s manual, version 4.0 - LAPTh

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1. Y where Y denotes equilibrium abundence evolution equation takes a form AY ds C Ay TD AY Qur T AY AY 12 35 jo TUTTPTTTT TTI T TT Ty tr ar ttt pri irr 0 2 a 0 1 2 3 4 5 6 10 Br b gt sy Figure 1 Relative difference for B B sy between micromegas2 4 and superlso3 1 the vertical lines show the 30 experimentally measured value where ue C 38H 13 lt 2 ra 2 72100 4 gH E qe E 14 o2 AWRY 2 020 oP o 0 501 of PEL Y 7 100 oi he 120 0 a 7 ae 15 git i122 1 g1210 Qe aA gam 16 17 At large temperatures we expect the densities of both DM components to be close to their equilibrium values Here solution can be presented in the form AY s Aj s Cj s 18 where exponential factors in A and C are cancell one other thus AY s slow depends on temperature that retroactively justifies neglecting of left part of Eq 12 Solution 18 can be used as a stating point for complete Eq 12 In general in micrOMEGAs 1 the equation for the abundance is solved numerically starting from large temperatures However this procedure poses a problem for Eq 12 The step of the numerical solution is inversely proportional to A T and as long as A T is not suppressed by the Boltzmann factor included in Y the step is too small and the numerical method fails To avoid this problem we use the fact that at large temperatures one can neglect th
2. _generated storage of matrix elements generated by CalcHEP calchep directory for interactive CalcHEP sessions Directories of other models which have the same structure as MSSM NMSSM CPVMSSM IDM LHM RHNM SM4 Z3M Z4ID mdlIndep Next to Minimal Supersymmetric Model 23 17 MSSM with complex parameters 26 16 Inert Doublet Model 8 Little Higgs Model 7 Right handed Neutrino Model 21 Toy model with a 4th generation of lepton and neutrino DM A model with scalar DM and Z3 discrete symmetry 9 42 A model with Z4 symmetry 9 42 For model independent computation of DM signals 3 2 Compilation of CalcHEP and micrOMEGAs routines CalcHEP and micrOMEGAs are compiled by gmake Go to the micrOMEGAs directory and launch gmak If gmake is e not available then make should work like gmake In principle micrOMEGAs defines automatically the names of C and Fortran compilers and the flags for compila tion If you meet a problem open the file which contains the compiler specifications CalcHEP_s rc FlagsForSh improve it and launch g make again The file is written is sh script format and looks like C compiler CC gcc Flags for C compiler CFLAGS g fsigned char Disposition of header files for X11 HX11 Disposition of 1X11 LX11 1X11 Fortran compiler FC gfortran FFLAGS fno automatic After a successful definition of compilers and their flags micrOMEGAs rewrites the file Flag
3. computes the ratio of the MSSM to SM value for R3 in A uv due to a charged higgs contribution see Eq 70 in 6 e dtaunu amp dmunu computes the branching ratio for D rtv dmunu gives the branching ratio for D gt Wy e masslimits returns a positive value and prints a WARNING when the choice of parameters conflicts with a direct accelerator limits on sparticle masses from LEP The constraint on the light Higgs mass from the LHC is included We have added a routine for an interface with superIso 32 This code is not included in micrOMEGAs so one has first to define the global environment variable superIso to specify the path to the package e callSuperIsoSLHA launches superIso and downloads the SLHA file which contains the results The return value is zero when the program was executed successfully Results for specific observ ables can be obtained by the command slhaValFormat described in section 13 5 Both superIso and callSuperIsoSLHA use a file interface to exchange data The delFiles flag specifies whether to save or delete the intermediate files 25 e loopGamma amp vcs_gz amp vcs_gg calculates ov for loop induced processes of neutralino annihilation into yZ and into yy The result is given in In case of a problem the function returns a non zero value 12 2 The NMSSM As in the MSSM there are specific routines to compute the parameters of the model as specified in SLHA The spectrum calculator i
4. value if it cannot recognize a parameter name e findValW name just returns the value of variable name and writes an error message if it cannot recognize a parameter name The variables accessible by these commands are all free parameters and the constrained parameters of the model in file model func1 md1 treated as public The following routines are used to display the value of the independent and the con strained public parameters e printVar FD prints the numerical values of all independent and public constrained parameters into FD e printMasses FD sort prints the masses of odd particles those whose names started with If sort 0 the masses are sorted so the mass of the CDM is given first e printHiggsMasses FD sort prints the masses and widths of even scalars 10 6 Relic density calculation 6 1 Switches and auxilary routines eVWdecay VZdecay Switches to turn on off processes with off shell gauge bosons in the final state for DM an nihilation and particle decays If VW VZdecay 1 the 3 body final states will be computed for annihilation processes only while if VW VZdecay 2 they will be included in coanni hilation processes as well By default the switches are set to VW VZdecay 1 Note that micrOMEGAs calculates the width of each particle only once and stores the result in Decay Table A second call to the function pWidth whether an explicit call or within the computation of a cross section will retu
5. SigmaFFPd 0 23 SigmaFFNd_ 0 84 SigmaFFPu 0 84 SigmaFFNu_ 0 23 Tensor form factor SigmaFFPs 0 046 SigmaFFNs 0 046 Table 3 Evaluated global variables Name units comments Evaluated by CDM1 character name of first DM particle sortOddParticles CDM2 character name of second DM particle sortOddParticles Mcdm1 GeV Mass of the first Dark Matter particle sortOddParticles Mcdm2 GeV Mass of the second DM particles sortOddParticles Mcdm GeV min Mcdm1 Mcdm2 if both exist sortOddParticles dmAsymm Asymmetry between relic density of DM DM darkOmega FO fracCDM2 fraction of CDM2 in relic density darkOmega2 e assignVal name val e assignValW name val assign value val to parameter name The function assignVal returns a non zero value if it cannot recognize a parameter name while assignValW writes an error message e readVar fileName reads parameters from a file The file should contain two columns with the following format see also Section 3 5 name value readVar returns zero when the file has been read successfully a negative value when the file cannot be opened for reading and a positive value corresponding to the line where a wrong file record was found Note that in Fortran numerical constants should be specified as Real 8 for example call assignValW SW 0 473D0 A common mistake is to use Real 4 The constrained parameters of the model are stored in w
6. This function is similar to nucleusRecoil The additional input parameters include csIp csIn the SI cross sections for WIMP scattering on protons neutrons and csDp csDn the SD cross sections on protons neutrons A negative value for one of these cross sections is interpreted as a destructive interference between the proton and neutron amplitudes Note that the rate of recoil depends implicitly on the WIMP mass the global parameter Mcdm The numerical value for the global parameter has to be set before calling this func tion e nucleusRecoil0Aux f A Z J Sp Sn csIp csIn csDp csDn dNdE is the correspond ing modification of nucleusRecoil0 For indirect detection we also provide a tool for model independent studies e basicSpectra pdgN outN Spectr computes the spectra of outgoing particles and writes the result in an array of dimension 250 Spectr pdgN is the PDG code of the particles produced in the annihilation of a pair of WIMPs To get the spectra generated by transverse and longitudinal W s substitute pdgN 24 T and 24 L correspondingly In the same manner pdgN 23 T and 23 L provides the spectra produced by a polarized Z boson outN specifies the outgoing particle outN 0 1 2 3 4 5 for 7 e p7 Ve Vu Vr This function depends implicitly on the global variable Mcdm Note that the propaga tion routines for e p 7 can be used after this routine as usual Note that the result of basicSpectra are no
7. a routine which calculates nucleus form factors for spin dependent interac tions S00 S01 S11 it depends on the momentum transfer in fmt The available form factors are SxxF19 SxxNa23 SxxNa23A SxxA127 SxxSi29 SxxSi29A SxxK39 SxxGe73 SxxGe73A SxxNb92 SxxTe125 SxxTe125A SxxI127 SxxI127A SxxXe129 SxxXei29A SxxXe131 SxxXe131A SxxXe131B The last character is used to distinguish different implementations of the form factor for the same isotope see details in 4 qBOX a parameter needed by nucleonAmplitudes see the description above The form factors for the spin independent SI cross section are defined by a Fermi dis tribution and depend on the global parameters Fermi_a Fermi_b Fermi_c The returned value gives the number of events per day and per kilogram of detector material The result depends implicitly on the global parameter rhoDM the density of DM near the Earth The distribution over recoil energy is stored in the array dNdE which by default has Nstep 200 elements The value in the it element corresponds to 4 dN dNdE i TE BaiskeVstep in units of 1 keV kg day By default step is set to 1 For a complex WIMP nucleusRecoil averages over y and Y For example for Ge a call to this routine will be nucleusRecoil Maxwell 73 Z_Ge J_Ge73 SxxGe73 FeScLoop dNdE 15 e setRecoilEnergyGrid step Nstep changes the values of step and Nstep for the computation of dNdE e Maxwell v returns 7 5 v VEa
8. between the direction of observation and the direction to the center of Earth E is the muon energy in GeV e ATMmuonContained cosFi E rho calculates the muon flux caused by atmospheric neutrinos produced in a given detector volume The returned value for the flux is given in 1 Year km GeV rho is the density of the detector in g cm units cosFi and E are the same as above 10 Cross sections and decays The calculation of particle widths decay channels and branching fractions can be done by the function e pWidth particleName amp address returns directly the particle width If the 1 gt 2 decay channels are kinematically accessible then only these channels are included in the width when VWdecay VZdecay 0 If not pWidth compiles all open 1 gt 3 channels and use these for computing the width If all 1 gt 3 channels are kinematically forbidden micrOMEGAs compiles 1 gt 4 channels If VWdecay VZdecay 0 then micrOMEGAs also computes the processes with virtual W Z which are closed kinematically and adds these to the 1 gt 2 decay channels Note that 1 gt 3 decay channels with a virtual W will be computed even if the mass of the decaying particle exceeds the threshold for 1 gt 2 decays by several GeV s This is done to ensure a proper matching of 1 gt 2 and 1 gt 3 processes For particles other than gauge bosons an improved routine with 3 body processes and a matching between the 1 gt 2 and 1 gt 3 calculations is kept for the f
9. example in MSSM calchep models func2 mdl Note that in this example the call to slhaRead is done within the function suspectSUGRAc 13 5 1 Writing an SLHA input file We have included in the micrOMEGAs package some routines which allow to write an SLHA input file and launch the spectrum generator via the CalcHEP constraints menu This way a new model can be implemented without the use of external libraries The routines are called from func1 mdl see example below e openAppend fileName deletes the input file fileName and stores its name This file will then be filled with the function aPrintF e aPrintF format opens the file fileName and writes at the end of the file the input parameters needed in the SLHA format or in any other format understood by the spectrum calculator The arguments of aPrintF are similar to the arguments of the standard printf function e System command generates a command line which is launched by the standard system C function The parameter command works here like a format string and can contain s Yd elements These are replaced by the next parameters of the System call For example to write directly the SLHA model file needed by SuSpect to compute the spectrum in a CMSSM SUGRA model one needs to add the following sequence in the func1 md1 model file open openAppend suspect2_lha in inputi aPrintF Block MODSEL Select model n 1 1 SUGRA n input2 aPrintF Block SMINPUTS n 5 E mb
10. extension of the SLHA interface to transfer Flavour Physics data 31 Unfortunately the structure of the new blocks is such that they cannot be read with the slhaVal routine We have added two new routines for reading such data e slhaValFormat BlockName Q format where the format string allows to specify data which one would like to extract from the given block BlockName For instance to get the b sy branching ratio from the block Block FOBS Flavour observables ParentPDG type value q NDA ID1 ID2 ID3 comment 5 1 2 95061156e 04 0 2 3 22 BR b gt s gamma 521 4 8 35442304e 02 0 2 313 22 Delta0 B gt K gamma 531 1 3 24270419e 09 0 2 13 F713 BR B_s gt mu mu one has to use the command slhaValFormat FOBS 0 5 1 E 0 2 3 22 In this command the format string is specified in C style The same routine can be used to read HiggsBound SLHA output A block can also contain a textual information For example in HIGGSBOUNDS a block contains the following records Block HiggsBoundsResults CHANNELTYPE 1 channel with the highest statistical sensitivity 1 1 328 channel id number 1 2 1 HBresult 1 3 0 72692779334500290 obsratio 1 4 1 ncombined 1 5 p p gt h h 1 where h is SM like CMS PAS HIG 12 008 text description of channel In particular the last record contains the name of the channel which gives the strongest constraint on the Higgs To extract the name of this channel one can use the new
11. mb n 6 E mt pole n MbMb Mtp input3 aPrintF BLOCK MINPAR n 1 E mO n 2 ZE m1 2 n Mzero Mhalf input4 aPrintF 3 ZE tb n 4 VE sign mu n 5 ZE A0 n tb sgn A0 sys System suspect2 exe rd slhaRead suspect2_lha out 0 It is possible to cancel the execution of a program launched with System if it runs for too long For this we have introduced two global parameters sysTimeLim and sysTimeQuant sysTimeLim sets a time limit in milliseconds for System execution if sysTimeLim 0 the default value the execution time is not checked The time interval between checks of the status of the program launched with System is specified by the parameter sysTimeQuant the default value is set to 10 Note that it is preferable not too use too large a value for sysTimeQuant as it defines the lower time limit for a system call In Fortran use call setSysTimeLim sysTimeLim sysTimeQuant to reset the default time control parameters The function prototypes are available in CalcHEP_src c_source SLHAplus include SLHAplus h 32 13 6 Routines for diagonalisation Very often in a new model one has to diagonalize mass matrices Here we present some numerical routines for diagonalizing matrices Our code is based on the jacobi routine provided in 30 To use the same routine for a matrix of arbitrary size we use a C option that allows to write routines with an arbitrary number of arguments e initDiagonal should be called once before any other rDi
12. routine that gives the relative contribution of each channel to Qh see printChannels below The fast 1 flag forces the fast calculation for more details see Ref 2 This is the recommended option and gives an accuracy around 1 The parameter Beps defines the criteria for including a given coannihilation channel in the computation of the ther mally averaged cross section 2 The recommended value is Beps 1074 107 whereas if Beps 1 only annihilation of the lightest odd particle is computed e darkOmegaFO amp Xf fast Beps calculates the dark matter relic density Qh using the freeze out approximation Both darkOmega and darkOmegaFO set parameter fracCDM2 0 or 1 depending on the name of lightest odd particle e printChannels Xf cut Beps prcnt FD writes into FD the contributions of different channels to Qh Here Xf is an input parameter which should be evaluated first in darkOmega F0 Only the channels whose relative contribution is larger than cut will be displayed Beps plays the same role as the darkOmega FO routine If prent 0 the contributions are given in percent Note that for this specific purpose we use the freeze out approximation e oneChannel Xf Beps p1 p2 p3 p4 calculates the relative contribution of the channel p1 p2 p3 p4 to Oh pl p4 are particle names To sum over several channels one can write instead of a particle name e g in place of pl 12 e omegaCh is an array that conta
13. the discrete symmetry Xg 0 In the following all particles with charge X4 4 0 will be called odd and the lightest odd particle will be stable If neutral it can be considered as a DM candidate Typical examples of discrete symmetries used for constructing single DM models are Z2 and Z3 Multi component DM can arise in models with larger discrete symmetries A simple example is a model with Z x Z symmetry the particles charged under Z2 Z will belong to the first second dark sector The lightest particle of each sector will be stable and therefore a potential DM candidate Another example is a model with a Z4 symmetry The two dark sectors contain particles with Xg 1 4 and X4 1 2 respectively The lightest particle with charge 1 4 is always stable while the lightest particle of charge 1 2 is stable only if its decay into two particles of charge 1 4 is kinematically forbidden micrOMEGAs assumes that all odd particles have names starting with for example o1 for the lightest neutralino In versions 4 X to distinguish the particles with different transformation properties with respect to the discrete group that is particles belonging to different dark sectors we use the convention that the names of particles in the second dark sector starts with Note that micrOMEGAs does not check the symmetry of the Lagrangian it assumes that the name convention correctly identifies all particles with the same discrete symmet
14. to run micrOMEGAs with the exception of the new model files e The new model files in the CalcHEP format should then be included in the sub directory MODEL work models The files needed are vars1 mdl funci mdl prtclsi mdl lgrngi mdl extlib1 mdl For more details on the format and con tent of model files see 19 e For odd particles and for the Higgs sector it is recommended to use the widths that are automatically calculated internally by CalcHEP micrOMEGAs For this one has to add the symbol before the definition of the particle s width in the file prtclsi mdl for example Full name P aP PDG 2 spin mass width color Higgs 1 hi Ihi 125 KO Mhi I whi 1 e Some models contain external functions if this is the case they have to be com piled and stored in the MODEL lib aLib a library These functions should be written in C and both functions and their arguments have to be of type double The library aLib a can also contain some functions which are called directly from the main program The MODEL Makefile automatically launches make in the lib directory and compiles the external functions provided the prototypes of these ex ternal functions are specified in MODEL lib pmodel h The user can of course rewrite his own lib Makefile if need be If the new aLib a library needs some other libraries their names should be added to the SSS variable defined in MODEL Makefile 27 The MODEL directory contains both C an
15. Date July 22 2014 The micrOMEGAs user s manual version 4 0 G B langer F Boudjema A Pukhov A Semenov 1 LAPTH Univ de Savoie CNRS B P 110 F 74941 Annecy le Vieux France 2 Skobeltsyn Inst of Nuclear Physics Moscow State Univ Moscow 119992 Russia 3 Joint Institute for Nuclear Research JINR 141980 Dubna Russia Abstract We give an up to date description of the micrOMEGAs functions Only the routines which are available for the users are described Examples on how to use these functions can be found in the sample main programs distributed with the code Contents Introduction Discrete symmetry in micrOMEGAs Downloading and compilation of micrOMEGAs 3 1 File structure of micrOMEGAS 6 4 a4 4 a we we we 3 2 Compilation of CalcHEP and micrOMEGAs routines 3 3 Module structure of main programs 2 28 e 244 28 54 3 4 Compilation of codes for specific models 3 5 Command line parameters of main programs Global Parameters Setting of model parameters spectrum calculation parameter display Relic density calculation 6 1 Switches and auxilary routines es ava bob Se S484 eee SEERA 6 2 Calculation of relic density for one component Dark Matter models 6 3 Calculation of relic density for two component Dark Matter models Direct detection 7 1 Amplitudes for elastic scattering 64254 4444484444 444 8 T2 Scatte
16. It has to be called before any of these functions The input parameters are the QCD coupling at the Z scale a Mz the quark masses m m mo mp and m pole e alphaQCD Q calculates the running a at the scale Q in the MS scheme The calculation is done using the NNLO formula in 22 Thresholds for the b quark and t quark are included in ny at the scales mp m and m m respectively e MtRun Q MbRun Q McRun Q calculates top bottom and charm quarks running masses evaluated at NNLO e MtEff Q MbEff Q McEff Q calculates effective top bottom and charm quark masses using 22 M Q M Q 1 5 67a 35 94 1 36n5 a 164 14 ns 25 77 0 259n s a 8 where a a Q a M Q and a Q are the quark masses and running strong coupling in the MS scheme In micrOMEGAs we use the effective quark masses calculated at the scale Q 2Mcdm In some special cases one needs a precise treatment of the light quarks masses The function e MqRun M2GeV Q returns the running quark mass defined at a scale of 2 GeV The corresponding effective mass needed for the Higgs decay width is given by e Mqeff M2GeV Q 13 5 SLHA reader Very often the calculation of the particle spectra for specific models is done by some external program which writes down the particle masses mixing angles and other model parameters in a file with the so called SLHA format 18 14 The micrOMEGAs program contains routines for reading file
17. OMEGAs contain some specific routines which we describe here for the sake of completeness The current distribution includes the following models MSSM NMSSM CPVMSSM IDM inert doublet model LHM little Higgs model RHNM a Right handed Neutrino model SM4 toy model with 4th generation lepton and Z3M doublet and singlet model with Z symmetry Some of these models contain a special routine for reading the input parameters e readVarMSSM readVarNMSSM readVarCPVMSSM readVarlHiggs readVarRHNM These routines are similar to the general readVar routine described in Section 5 but they write a warning when a parameter is not found in the input file and display the default values for these parameters The supersymmetric models contain several additional routines to calculate the spec trum and compute various constraints on the parameter space of the models Some functions are common to the MSSM NMSSM CPVMSSM models e o1Contents FD prints the neutralino LSP components as the B W h h fractions For the NMSSM the fifth component is the singlino fraction S The sum of the squares of the LSP components should add up to 1 12 1 MSSM The MSSM has a long list of low scale independent model parameters those are specified in the SLHA file 18 14 They are directly implemented as parameters of the model For EWSB scenarios the input parameters are the soft parameters the names of these parameters are given in the MSSM mssm 1 2 par fil
18. agonal A routine described below initDiagonal assigns zero value to the internal counter of eigenvalues and rotation matrices Returns zero e rDiagonal d M11 M12 M1d M22 M23 Mdd diagonalizes a symmetric matrix of dimension d The d d 1 2 matrix elements Mij i lt j are given as arguments The function returns an integer number id which serves as an identifier of eigenvalues vector and rotation matrix e MassArray id i returns the eigenvalues m ordered according to their absolute values e MixMatrix id i j returns the rotation matrix R where Mi yo RkiMmk Rki k A non symmetric matrix for example the chargino mass matrix in the MSSM is diagonalized by two rotation matrices Mi D Uti Viegs k e rDiagonalA d M11 M12 M1d M21 M22 Mdd diagonalizes a non symmetric matrix the d matrix elements Mij are given as arguments The eigenvalues and the V rotation matrix are calculated as above with MassArray and MixMatrix e MixMatrixU id i j returns the rotation matrix U j The function prototypes can be found in CalcHEP_src c_source SLHAplus include SLHAplus h 14 Mathematical tools Some mathematical tools used by micrOMEGAs are available only in C format Prototypes of these functions can be found in sources micromegas_aux h e simpson F x1 x2 eps numerical integration of the function F x in the interval 71 22 with relative precision eps simpson uses an adaptive algorithm for integrand eval
19. alaxy as well as on the annihilation spectrum into photons e gammaFluxTab fi dfi sigmav Sg Sobs multiplies the annihilation photon spectrum with the integral over the line of sight and over the opening angle to give the photon flux fi is the angle between the line of sight and the center of the galaxy dfi is half the cone angle which characterizes the detector resolution the solid angle is 27 1 cos dfi sigmav is the annihilation cross section Sg is the DM annihilation spectra Sobs is the spectra observed The function gammaFluxTab can be used for the neutrino spectra as well e gammaFlux fi dfi vcs is the same function as gammaFluxTab above but corresponds to a discrete photon spec trum vcs is the annihilation cross section for instance in the MSSM it is calculated with the loopGamma function The function returns the number of photons per cm of detector surface per second Note that for yx yy the result should be multiplied by a factor 2 as each annihilation leads to the production of two photons 8 5 Propagation of charged particles The observed spectrum of charged particles strongly depends on their propagation in the Galactic Halo The propagation depends on the global parameters K_dif Delta_dif L_dif Rsun Rdisk as well as Tau_dif positrons Vc_dif antiprotons e posiFluxTab Emin sigmav Se Sobs computes the positron flux at the Earth Here sigmav and Se are values obtained by calcSpectrum Sobs is the posi
20. arkOmega routine The returned value corresponds to the sum of the contribution of the two DM components to Qh darkOmega2 also calculates the global parameter fracCDM2 which represents the mass fraction of CDM2 in the total relic density Q 14M 1 Q fracCDM2 a 2 This parameter is then used in routines which calculate the total signal from both DM can didates in direct indirect and neutrino telescope experiments nucleusRecoil calcSpectrum and neutrinoFlux The user can change the global fracCDM2 parameter before the calcu lation of these observables to take into account the fact that the value of the DM fraction in the Milky Way could be different than in the early Universe The routines that were described in section 6 2 are not available for two component DM models In particular the individual channel contribution to the relic density cannot be computed and DM asymmetry is ignored After calling darkOmega2 the user can check the cross sections for each class of reactions but not for individual processes which were tabulated during the calculation of the relic density The functions evsaabbF T computes the sum of cross sections for each class of reactions a b 0 1 2 tabulated during the calculation of the relic density Here T is the temperature in GeV and the 13 return value is vo in pb These functions are defined in the interval Tstart Tend where Tstart is defined by darkOmega2 Tend 10 GeV Specifically the fu
21. ation parameter display The independent parameters that characterize a given model are listed in the file work models vars1 mdl Three functions can be used to set the value of these parame ters Table 1 Global input parameters of micrOMEGAs Name default value units comments deltaY 0 Difference between DM anti DM abundances K_dif 0 0112 kpc Myr The normalized diffusion coefficient L_dif 4 kpe Vertical size of the Galaxy diffusive halo Delta_dif 0 7 Slope of the diffusion coefficient Tau_dif 1016 s Electron energy loss time Vc_dif 0 km s Convective Galactic wind Fermi_a 0 52 fm nuclei surface thickness Fermi_b 0 6 fm parameters to set the nuclei radius with Fermi_c 1 23 fm Ra cA b Rsun 8 5 kpe Distance from the Sun to the center of the Galaxy Rdisk 20 kpe Radius of the galactic diffusion disk rhoDM 0 3 GeV cm Dark Matter density at Rsun Vearth 220 2 km s Galaxy velocity of the Earth Vrot 220 km s Galaxy rotation velocity at Rsun Vesc 600 km s Escape velocity at Rsun Table 2 Global parameters of micrOMEGAs nucleon quark form factors Proton Neutron Name value Name value comments ScalarFFPd 0 0191 ScalarFFNd_ 0 0273 ScalarFFPu 0 0153 ScalarFFNu 0 011 Scalar form factor ScalarFFPs 0 0447 ScalarFFNs 0 0447 pVectorFFPd 0 427 pVectorFFNd 0 842 pVectorFFPu 0 842 pVectorFFNu 0 427 Axial vector form factor pVectorFF Ps 0 085 pVectorFFNs 0 085
22. c density in case of 2 DM components 20 21 22 24 24 26 26 27 27 28 28 29 29 32 33 33 34 35 1 Introduction micrOMEGAs is a code to calculate the properties of cold dark matter CDM in a generic model of particle physics First developed to compute the relic density of dark mat ter the code also computes the rates for dark matter direct and indirect detection micrOMEGAs calculates CDM properties in framework of a model of paricles interac tion presented in CalcHEP format 19 It is assumed that the model is invariant ander a discrete symmetry like R parity which is even for all standard particles and odd for some new particles including the dark matter candidate ensures the stability of the lightest odd particle LOP CalcHEP package is included in micrOMEGAs and used for matrix elements calculations All annihilation and coannihilation channels are included in the computation of the relic density This manual gives an up to date description of all micrOMEGAs functions The methods used to compute the different dark matter prop erties are described in references 1 2 3 4 5 6 These references also contain a more complete description of the code In the following the cold dark matter candidate also called LOP or weakly interactive massive particle WIMP will be denoted by y micrOMEGAs contains both C and Fortran routines Below we describe only the C version of the routines in general we use the same nam
23. d FORTRAN samples of main routines In these sample main programs it is assumed that input parameters are provided in a separate file In this case the program can be launched with the command main data1 par Note that for the direct detection module all quarks must be massive However the cross sections do not depend significantly on the exact numerical values for the masses of light quarks 13 2 Automatic width calculation Automatic width calculation can be implemented by inserting the symbol before the name of the particle width in the CalcHEP particle table file prtclsl mdl In this case the width parameter should not be defined as a free or constrained parameter Actually the pWidth function described in section 10 is used for width calculation in this case We recommend to use the automatic width calculation for all particles from the odd sector and for Higgs particles For models which use SLHA parameter transfer Section 13 5 the automatic width option will use the widths contained in the SLHA file unless the user chooses the option to ignore this data in the SLHA file see section 13 5 13 3 Using LanHEP for model file generation For models with a large number of parameters and various types of fields particles such as the MSSM it is more convenient to use an automatic tool to implement the model LanHEP is a tool for Feynman rules generation A few minor modifications to the de fault format of LanHEP have to be ta
24. d code for further usage If the process can not be compiled then a NULL address is returned Note that it is also possible to compute processes with polarized massless beams for example for a polarized electron beam use e to designate the initial particle e procInfol address amp ntot nin knout provides information about the total number of subprocesses ntot stored in the library specified by address as well as the number of incoming nin and outgoing nout parti cles for these subprocesses Typically for collisions decays nin 2 1 and nout 2 3 NULL can be substitute if this information is not needed e procInfo2 address nsub N M fills an array of particle names N and an array of particle masses M for the subprocess nsub 1 lt nsub lt ntot These arrays have size nin nout and the elements are listed in the same order as in CalcHEP starting with the initial state see the example in MSSM main c e cs22 address nsub P c1 c2 kerr calculates the cross section for a given 2 2 process nsub with center of mass momen tum P GeV The differential cross section is integrated within the range cl lt cos lt c2 0 is the angle between p and p3 in the center of mass frame Here p p3 denote respec tively the momentum of the first initial final particle err contains a non zero error code if nsub exceeds the maximum value for the number of subprocesses given by the argu ment ntot in the routine procInfo1 To
25. e Q term in Eq 12 and write the explicit solution for the linearised equation The 36 approximate solution in the case of large A is One can use Eq 18 to find the lowest temperature where AY 0 05Y and start solving numerically Eq 12 from this temper ature In the general case it gives a reasonable step for the numerical solution 6s s 0 1 where s is the variable of integration This method can however lead to some numerical problems if the masses of the two dark matter particles are very different Let us call the light particle and the heavy particle A We have to start the numerical solution at a temperature T above the freeze out temperature of the heaviest DM Thos xX M 25 19 At this temperature Y M T Me 20 7 exp _ Ya a Tiron and the step in the numerical solution of the two component equations will be suppressed by a factor exp M Mr Tos This small step size is problematic when solving numer ically the equation with the Runge Kutta method This occurs when M4 M r gt 2 In this case the equation for the heavy component must be solved independently assuming that the light component has reached its equilibrium density If M M lt 2 the Runge Kutta procedure can be used to successfully solve the thermal evolution equations 12 References 1 G Belanger F Boudjema A Pukhov and A Semenov Comput Phys Commun 149 2002 103 arXiv hep ph 0112278 N G Belanger F Bo
26. ecipes The Art of Scientific Computing Cambridge University Press 2007 31 F Mahmoudi et al arXiv 1008 0762 hep ph 38 32 A Arbey and F Mahmoudi Comput Phys Commun 182 2011 1582 33 M Misiak H M Asatrian K Bieri M Czakon A Czarnecki T Ewerth A Fer roglia P Gambino et al Phys Rev Lett 98 2007 022002 hep ph 0609232 34 M Misiak M Steinhauser Nucl Phys B764 2007 62 82 hep ph 0609241 35 P Gambino P Giordano Phys Lett B669 2008 69 73 arXiv 0805 0271 hep phi 36 W M Yao et al Particle Data Group Collaboration J Phys G G33 2006 1 1232 37 K Nakamura et al Particle Data Group Collaboration J Phys G G37 2010 075021 38 G Jungman M Kamionkowski and K Griest Phys Rept 267 1996 195 hep ph 9506380 39 M Cirelli N Fornengo T Montaruli I A Sokalski A Strumia and F Vissani Nucl Phys B 727 2005 99 Erratum ibid B 790 2008 338 hep ph 0506298 40 A E Erkoca M H Reno and I Sarcevic Phys Rev D 80 2009 043514 arXiv 0906 4364 hep ph 41 D Maurin R Taillet and C Combet astro ph 0609522 42 G Blanger K Kannike A Pukhov and M Raidal JCAP 1406 2014 021 arXiv 1403 4960 hep ph 39
27. er files are provided in the sources data directory HP_A_thg tab HP_B_thg tab HP_B2_thg tab HP_B3_thg tab and HP_C_thg tab They correspond to sets A B B2 B3 C in 10 The user can substitute his her own table as well if so the file must contain three columns containing the numerical values for T heff geff the data file can also contain comments for lines starting with eimproveCrossSection p1l p2 p3 p4 Pcm amp address allows to substitute a new cross section for a given process Here p1 p2 are the names of particles in the initial state and p3 p4 those in the final state Pcm is the center of mass momentum and address This function is useful if for example the user wants to include her his one loop improved cross section calculation in the relic density computation Including the 3 body final states can significantly increase the execution time for the relic density 11 6 2 Calculation of relic density for one component Dark Matter models All routines to calculate the relic density in version 3 are still available in this version For these routines the difference between the two dark sectors DM is ignored These routines are intended for models with either a Z or Z discrete symmetry e vSigma T Beps fast calculates the thermally averaged cross section for DM annihilation times velocity at a temperature T GeV see formula 2 6 in 1 The value for ov is expressed in pb The parameter Beps defines the crit
28. eria for including coannihilation channels as for darkOmega described below The fast 1 0 option switches between the fast accurate calculation The global array vSigmaTCh contains the contribution of different channels to vSigma vSigmaTCh i weight specifies the relative weight of the it channel vSigmaTCh i prtcl j j 0 4 defines the particles names for the it channel The last record in vSigmaTCh array has zero weight and NULL particle names In the For tran version the function vSigmaTCh i weight pdg process serves the same purpose This function returns 0 if exceeds the number of annihilation channels and 1 otherwise i gt 1 real 8 weight gives the relative contribution of each annihilation channel integer pdg 5 contains the codes of incoming and outgoing particles in the annihilation process character 40 process contains a textual description of annihilation processes The cross sections for semi annihilation processes contribute to vSigma with a factor 5 as described in 9 Furthermore if an outgoing particle has a non zero decay branching ratio to odd particles then the annihilation cross section is reduced correspondingly e darkOmega amp Xf fast Beps calculates the dark matter relic density Qh This routine solves the differential evolution equation using the Runge Kutta method X Mcdm T characterizes the freeze out temperature The value of X is given for information and is also used as an input for the
29. ermediate files define SHOWPLOTS Displays graphical plots on the screen Other modules which require a link to external programs can also be defined in this case the path to the required code must be specified for example define HIGGSBOUNDS Packages HiggsBounds 4 0 0 All these modules are completely independent The user can comment or uncomment any set of define instructions to suit his her need 3 4 Compilation of codes for specific models After the compilation of micrOMEGAs one has to compile the executable to compute DM related observables in a specific model To do this go to the model directory say MSSM and launch g make main main c It should generate the executable main In the same manner gmake main filename ext generates the executable filename based on the source file filename ezt For ext we sup port 3 options c F cpp which correspond to C FORTRAN and C sources g make called in the model directory automatically launches g make in subdirectories lib and work to compile lib aLib a library of auxiliary model functions e g constraints work work_aux a library of model particles free and dependent parameters 3 5 Command line parameters of main programs The default versions of main c F programs need some arguments which have to be spec ified in command lines If launched without arguments main explains which parameter are needed As a rule main needs the name of a file contai
30. es The user can assign new values to these parameters by means of assignVal or readVarMSSM e spectEwsbMSSM calculates the masses of Higgs and supersymmetric particles in the MSSM including one loop corrections starting from weak scale input parameters In these functions spect stands for one of the spectrum calculators suspect isajet spheno or softSusy The default spectrum calculator package is SuSpect To work with another package one has to specify the appropriate path in MSSM lib Makefile For this the environment variables ISAJET SPHENO or SOFTSUSY must be redefined accordingly Note that we also provide a special interface for ISAJET to read a SLHA file This means that the user must first compile the executable isajet_slha which sets up the SLHA interface in ISAJET Specific instructions are provided in the README file For other MSSM scenarios the parameters at the electroweak symmetry breaking scale are derived from an input at high scale The same codes suspect isajet spheno or softSusy are used for this The corresponding routines are e spectSUGRA tb MG1 MG2 MG3 A1 At Ab signMu MHu MHd M11 M13 Mri1 Mr3 Mq1 Mq3 Mui Mu3 Md1 Md3 assumes that all input parameters except tb and signMu are defined at the GUT scale The SUGRA CMSSM scenario is a special case of this general routine e spectSUGRAnuh tb MG1 MG2 MG3 A1 At Ab M11 M13 Mr1 Mr3 Mq1 Mq3 Mui Mu3 Md1 Md3 mu MA 24 realizes a SUGRA scenario with non universal H
31. es and the same types of argument for both C and Fortran functions We always use double real 8 variables for float point numbers and int INTEGER for integers In this manual we use FD for file descriptor variables the file descriptors are FILE in C and channel number in Fortran The symbol amp before the names of variables in C functions stands for the address of the variable It is used for output parameters In Fortran calls there is no need for amp since all parameters are passed via addresses In C programs one can substitute NULL for any output parameter which the user chooses to ignore In Fortran one can substitute cNull iNull r8Null for unneeded parameters of character integer and real 8 type respectively A few C functions use pointer variables that specify an address in the computer mem ory Because pointers do not exist in Fortran one uses any other type of variable whose length is sufficient to store a computer address for example INTEGER S The complete format for all functions can be found in sources micromegas h for C or sources micromegas_f h for Fortran Examples on how to use these functions are provided in the MSSM main c F file 2 Discrete symmetry in micrOMEGAs micrOMEGAs exploits the fact that models of dark matter exhibit a discrete symmetry and that the fields of the model transform as e d where the charge X lt 1 The particles of the Standard Model are assumed to transform trivially under
32. etection are stored in arrays with NZ 250 elements To decode and interpolate the spectrum array one can use the following functions e SpectdNdE E spectTab interpolates the tabulated spectra and returns the particle distribution dN dE where E is the energy in GeV For a particle number distribution the returned value is given in GeV units while a particle flux is expressed in sec cm sr GeV 71 To display the spectra as a function of energy one can use e displaySpectrum spectTab message Emin Emax 16 where message is a text string which gives a title to the plot and Emin and Emax define energy cuts Although structure of spectrum array actually does not need for the user we present it below The first zeroth element of array contains the maximum of spectrum energy Emax AS a rule Emar is a mass of DM particle The i element 1 lt i lt NZ 1 of the spectrum array contains the value of E where E Emare e Zi i 7 EL log 10 That is the array points cover the energy interval Emax gt E gt 10 Emaz 8 2 Annihilation spectra e calcSpectrum key Sg Se Sp Sne Snm Snl amp err calculates the spectra of DM annihilation at rest and returns ov in cm s The calculated spectra for y e P Ve Vu Vy are stored in arrays of dimension NZ as described above Sg Se Sp Sne Snm Snl To remove the calculation of a given spectra substitute NULL for the corresponding argument key is a switch to include the polarisa
33. function e slhaSTRFormat HiggsBoundsResults 1 5 7 1 channel which will write the channel name in the text parameter channel e slhaWarnings fileName writes into the file the warnings or error message stored in the SPINFO block and returns the number of warnings If FD NULL the warnings are not written in a file e slhaWrite fileName writes down the information stored by readSLHA into the file This function can be used for testing purposes SLHA also describes the format of the information about particle decay widths Even though micrOMEGAs also performs the width calculation one might choose to read the information from the SLHA file e slhaDecayExists pNum checks whether information about the decay of particle pNum exists in the SLHA file pNum is the particle PDG code This function returns the number of decay channels In particular zero means that the SLHA file contains information only about the total width not on branching ratios while 1 means that even the total width is not given e slhaWidth pNum returns the value of particle width e slhaBranch pNum N nCh returns the branching ratio of particle pNum into the N th decay channel Here 31 0 lt N lt slhaDecayExists pNum The array nCh is an output which specifies the PDG numbers of the decay products the list is terminated by zero The functions slhaValExists slhaVal slhaDecayExists slhaWidth can be used directly in CalcHEP model files see an
34. iggs parameters Here the Mhu MHd parameters in the Higgs potential are replaced with the mu parameter defined at the EWSB scale and MA the pole mass of the CP odd Higgs The signMu parameter is omitted because mu is defined explicitly espectAMSB amO m32 tb sng does the same as above within the AMSB model We have an option to directly read a SLHA input file this uses the function e lesHinput file_name which returns a non zero number in case of problem The routines for computing constraints are see details in 2 e deltarho calculates the Ap parameter in the MSSM It contains for example the stop sbottom contributions as well as the two loop QCD corrections due to gluon exchange and the correction due to gluino exchange in the heavy gluino limit e bsgnlo amp SMbsg returns the value of the branching ratio for b sy see Appendix A We have included some new contributions beyond the leading order that are especially important for high tan 3 SMbsg gives the SM contribution e bsmumu returns the value of the branching ratio B gt pty in the MSSM It includes the loop contributions due to chargino sneutrino stop and Higgs exchange The Amy effect rele vant for high tan is taken into account e btaunu computes the ratio between the MSSM and SM branching fractions for Bt gt rtv e gmuon returns the value of the supersymmetric contribution to the anomalous magnetic moment of the muon e R123
35. ins the relative contribution and particle names for each annihilation channel In the Fortran version one uses instead the function omegaCh i weight pdg process These array and function are similar to vSigmaTCh described above The array omegaCh if filled after calling either darkOmegaFO or printChannels There is an option to calculate relic density in models with DM DM asymmetry In this case we assume that the number difference DM DM is conserved in reactions Thus initial small difference in abundances can lead to large DM asymmetry after freeze out similar to baryonic asymmetry edeltaY describes the difference between the DM and anti DM abundances for the models where number of DM particles minus number of anti DM ones is conserved in reactions of decay and collisions In such models deltaY is a constant during thermal evolution of Universe See Ref 6 edmAsymm is defined by equation 1 dmAsymm 2 and evaluated by micrOMEGAs while calculating the relic density with an initial asymmetry deltaY See 6 This parameter can also be reset after the relic density computation and will be taken into account for direct and indirect detection rates mep 6 3 Calculation of relic density for two component Dark Matter models edarkOmega2 fast Beps Calculates Qh for either one or two components DM models In the latter case it should give the same result as darkOmega The parameters fast and Besp have the same meaning as for the d
36. interpolation e bessk0 x The Bessel function of zero order of the second kind e displayFunc F x1 x2 title displays a plot of function F x in the x1 x2 interval title is a text which appears as the title of the plot e displayFunc10 F x1 x2 title displays F 10 in the x1 x2 interval A An updated routine for b sy in the MSSM The calculation of b sy was described in micromegas1 3 2 The branching fraction reads V Vi i OW en V 1H 20 where Qem 1 137 036 the factor Kyzro involves the photon energy cut off parameter 6 and f z 0 542 2 23 z 0 29 depends on z m m defined in terms of pole masses In the code the standard model and Higgs contribution at NLO were included as well as the leading order SUSY contributions However in the last few years the NNLO standard model contribution has been computed 33 and shown to lead to large corrections shifting the standard model value by over 10 It was also argued that the NNLO SM result could be reproduced from the NLO calculation by appropriately choosing the scale for the c quark mass 34 35 In this improved version of the bsgnlo routine we have changed the default value for the parameter z1 m ms where me is the MS running charm mass m mp Taking z 0 29 allows to reproduce the NNLO result It is therefore no longer necessary to apply a shift to the micromegas output of b sy to reproduce the SM value We have also updated
37. ixing matrices and parameters of the effective Higgs potential are read directly from CPsuperH 26 27 together with the masses and the mixing matrices of the neutralinos charginos and third generation sfermions Masses of the first two generations of sfermions are evaluated at tree level within micrOMEGAs in terms of the independent parameters of the model The routines for computing constraints are taken from CPsuperH 28 e bsgnlo bsmumu btaunu gmuon are the same as in the MSSM case e deltaMd deltaMs are the same as in the NMSSM case 26 e Bd11 computes the supersymmetric contribution to the branching fractions for Ba gt TTT in the CPVMSSM e ABsg computes the supersymmetric contribution to the asymmetry for B gt X y e EDMel EDMmu EDMT1 return the value of the electric dipole moment of the electron de the muon d and of Thallium dy in units of ecm 13 Tools for new model implementation It is possible to implement a new particle physics model in micrOMEGAs For this the model must be specified in the CalcHEP format micrOMEGAs then relies on CalcHEP to generate the libraries for all matrix elements entering DM calculations Below we describe the main steps and tools for implementing a new model 13 1 Main steps e The command newProject MODEL launched from the root micrOMEGAs directory creates the directory MODEL This directory and the subdirectories contain all files needed
38. ken into account to get the model files into the micrOMEGAs format e The lhep command has to be launched with the evl 2 flag lhep source_file evl 2 Such a flag provides the correct level of optimization for the model s Feynman rules e The default format for the file prtcls1 md1 which specifies the particle content has to be modified to include a column containing the PDG code of particles For this first add the following command in the LanHEP source code before specifying the particles prtcformat fullname Full Name name P aname aP pdg number spin2 mass width color aux texname gt LaTeX A lt atexname gt LateX A lt Then for each particle define the PDG code For instance vector Wt W CW boson pdg 24 mass MW width wW 28 e LanHEP does not generate the file extlib1 mdl micrOMEGAs works without this file but it is required for a CalcHEP interactive session The role of this file is to provide the linker with the paths to all user s libraries needed at compilation For example for the lib aLib a library define CALCHEP MODEL lib aLib a For examples see the extlib1 md1 files in the directory of the models provided 13 4 QCD functions Here we describe some QCD functions which can be useful for the implementation of a new model e initQCD alfsMZ McMc MbMb Mtp This function initializes the parameters needed for the functions listed below
39. nctions available are vs1100F vsl110F vs1120F vs1112F vsl122F vsl210F vsl211F vsl220F vsl222F vs2200F vs2210F vs2220F vs2211F vs2221F The temperature dependence of the equilibrium abundances can also be called by the user the functions are named Y_1 T and Y_2 T and are defined only in the interval T Tend Tstart The equilibrium abundances are accessible via the Yeq1 T Yeq2 T functions and the deviation from equilibrium by the functions dY1F T Y1F T Y1teq T and dY2F T Y2F T Y2F T 7 Direct detection 7 1 Amplitudes for elastic scattering e nucleonAmplitudes CDM qBOX pAsi pAsd nAsi nAsd calculates the amplitudes for CDM nucleon elastic scattering at zero momentum pAsi nAsi are spin independent amplitudes for protons neutrons whereas pAsd nAsd are the cor responding spin dependent amplitudes Each of these four parameters is an array of dimension 2 The zeroth first element of these arrays gives the x nucleon amplitudes whereas the second element gives y nucleon amplitudes Amplitudes are normalized such that the total cross section for either x or X cross sections is AMMA 1 sr 4 3 45D 2 Otot 7M Myy2 4 3 A 3 If qBOX NULL qBOX NoLoop in Fortran tree level amplitudes are computed In MSSM type models with a spin 1 2 WIMP and scalar squarks qBOX FeScLoop uses an im proved tree level calculation nucleonAmplitudes returns a value different from zero only when there is an internal pr
40. ne and two tildes respectively Mcdm1 and Mcdm2 are masses of these particles If we have only one kind of DM then for the absent component Mcdm 0 and CDM NULL in Fortran the string if filled by space symbols e qNumbers pName amp spin2 amp charge3 amp cdim returns the quantum numbers for the particle pName Here spin2 is twice the spin of the particle charge3 is three times the electric charge cdim is the dimension of the representation of SU 3 e it can be 1 3 3 or 8 The parameters spin2 charge3 cdim are variables of type int The value returned is the PDG code If pName does not correspond to any particle of the model then qNumbers returns zero e pdg2name nPDG returns the name of the particle which PDG code is nPDG If this particle does not exist in the model the return value is NULL In the FORTRAN version this function is Subroutine pdg2name nPDG pName and the character variable pName consists of white spaces if the particle does not exist in the model e pMass pName returns the numerical value of the particle mass e nextOdd n amp pMass returns the name and mass of the n odd particle assuming that particles are sorted ac cording to increasing masses For n 0 the output specifies the name and the mass of the CDM candidate In the FORTRAN version this function is Subroutine nextOdd n pName pMass e findVal name amp val finds the value of variable name and assigns it to parameter val It returns a non zero
41. ning the numerical values of the free parameters of the model The structure of a file record should be Name Value comment optional For instance an Inert Doublet model IDM input file contains Mh 125 mass of SM Higgs MHC 200 mass of charged Higgs H MH3 200 mass of odd Higgs H3 MHX 63 2 mass of X particle la2 0 01 lambda_2 coupling laL 0 01 0 5 lambda_3 lambda_4 lambda_5 In other cases different inputs can be required For example in the MSSM with input parameters defined at the GUT scale the parameters have to be provided in a command line Launching main will return This program needs 4 parameters mO common scalar mass at GUT scale mhf common gaugino mass at GUT scale a0 trilinear soft breaking parameter at GUT scale tb tan beta Auxiliary parameters are sgn 1 sign of Higgsino mass term default 1 Mtp top quark pole mass MbMb Mb Mb scale independent b quark mass alfSMZ strong coupling at MZ Example main 120 500 350 10 1 173 1 4 Global Parameters The list of the global parameters and their default values are given in Tables 1 2 The numerical value for any of these parameters can be simply reset anywhere in the code Numerical values of scalar quark form factors can also be reset by the calcScalarQuarkFF routine presented below Some physical values evaluated by micrOMEGAs also are pre sented as global variables See Table 3 5 Setting of model parameters spectrum calcul
42. o sets back the Zhao profile Note that both setProfileZhao and setProfileEinasto call setHaloProfile to define the cor responding profile Dark matter annihilation in the Galaxy depends on the average of the square of the DM density lt p gt This quantity can be significantly larger than lt p gt when clumps of DM are present 13 In micrOMEGAs we use a simple model where fa is a constant that characterizes the fraction of the total density due to clumps and where all clumps occupy the same volume V and have a constant density pa Assuming clumps do not overlap we get lt p gt p fePep 6 This simple description allows to demonstrate the main effect of clumps far from the Galactic center the rate of DM annihilation falls as p r rather than as p r The pa rameters pa and fa have zero default values The routine to change these values is e setClumpConst fa pe To be more general one could assume that pa and fa depend on the distance from the galactic center The effect of clumping is then described by the equation lt p gt r PNP Piiimp 7 and the function e setRhoClumps pff p allows to implement a more sophisticated clump structure To return to the default treatment of clumps call setRhoClumps rhoClumpsConst or setClumpConst 18 8 4 Photon signal The photon flux does not depend on the diffusion model parameters but on the angle between the line of sight and the center of the g
43. oblem in the calculation nucleonAmplitudes depends implicitly on form factors which describe the quark con tents in the nucleon These form factors are global parameters see Table 1 for default values TypeFFPq T ypeFFNq 2 9 where Type is either Scalar pVector or Sigma FFP and FFN denote proton and neutron and q specifies the quark d u or s Heavy quark coefficients are calculated automatically e calcScalarQuarkFF m ma M5 Md 0rNn 0s computes the scalar coefficients for the quark content in the nucleon from the quark mass ratios Mu Ma Ms Ma as well as from cry and o The default values given in Table 2 are obtained for 0 42MeV o y 34MeV m mqg 0 56 m mq 20 2 11 The function calcScalarQuarkFF 0 553 18 9 55 243 5 will reproduce the default values of the scalar quark form factors used in micrOMEGAs2 4 and earlier versions All parameters are in GeV 14 7 2 Scattering on nuclei e nucleusRecoil f A Z J Sxx qBOX dNdE This is the main routine of the direct detection module The input parameters are f the DM velocity distribution normalized such that vf v dv 1 The units are km s for v and s km for f v A atomic number of nucleus Z number of protons in the nucleus predefined values for a wide set of isotopes are called with Z_ Name J nucleus spin predefined values for a wide set of isotopes are called with J_ Name atomicnumber Sxx is
44. ork models func1 mdl Some of these parameters are treated as public parameters The public parameters in clude by default all particle masses and all parameters whose calculation requires external functions except simple mathematical functions like sin cos The parameters listed above any public parameters in work models func1 mdl are also treated as public It is possible to enlarge the list of public parameters There are two ways to do this One can type before a parameter name to make it public or one can add a special record in work models funci mdl Local Then all parameters listed above this record become public See example in MSSM work models func1 md1 The calculation of the particle spectrum and of all public model constraints is done with e sortOddParticles txt which also sorts the odd particles with increasing masses writes the name of the lightest odd particle in txt and assigns the value of the mass of the lightest odd particle to the global parameter Mcdm This routine returns a non zero error code for a wrong set of parameters for example parameters for which some constraint cannot be calculated The name of the corresponding constraint is written in txt This routine has to be called after a reassignment of any input parameter These routine was updated for the case of two DM particles sortOddParticles fills text parameters CDM1 and C DM2 which present the name of lightest particle which names are started with o
45. otons with gas of galactix disk It depends on proton flux and propagation parameters But all sets of propagation parameters corresponding to the measured B C rate should provide the same p p rate It gives an opportunity of robust estimation of anti proton background Function e pBarBackgroundF lux E calculates p backgraund flux in GeV cm s units using formula of 41 There is an option to present this flux as an array of the format used by micrOMEGAs for other fluxes e pBarBackgroundTab Emax pTab where Emax defines an energy cut Then one can apply to this array the solarModulation routine to take into account effect of solar modulation 1 9 Neutrino signal from the Sun and the Earth This module does not work yet in case of 2DM After being captured DM particles concentrate in the center of the Sun Earth and then annihilate into Standard Model particles These SM particles further decay produc ing neutrinos that can be observed at the Earth e neutrinoFlux f forSun nu nu_bar calculates muon neutrino anti neutrino fluxes near the surface of the Earth Here f is the DM velocity distribution normalized such that f uf v dv 1 The units are km s for v and s km for f v At first approximation one can use the same Maxwell function introduced for direct detection If forSun 0 then the flux of neutrinos from the Earth is calculated otherwise this function computes the flux of neutrinos from the Sun The calculated fluxe
46. r F Boudjema S Kraml A Pukhov and A Semenov Phys Rev D 73 2006 115007 arXiv hep ph 0604150 G Belanger F Boudjema C Hugonie A Pukhov and A Semenov JCAP 0509 2005 001 arXiv hep ph 0505142 18 P Skands et al JHEP 0407 2004 036 arXiv hep ph 0311123 19 A Pukhov arXiv hep ph 0412191 20 A Semenov Comput Phys Commun 180 2009 431 arXiv 0805 0555 hep ph 21 G Belanger A Pukhov and G Servant JCAP 0801 2008 009 arXiv 0706 0526 hep ph 22 S Eidelman et al Particle Data Group Phys Lett B 592 2004 1 23 U Ellwanger and C Hugonie Comput Phys Commun 177 2007 399 arXiv hep ph 0612134 24 U Ellwanger and C Hugonie Comput Phys Commun 175 2006 290 arXiv hep ph 0508022 25 F Domingo and U Ellwanger JHEP 0712 2007 090 arXiv 0710 3714 hep ph 26 J S Lee A Pilaftsis M S Carena S Y Choi M Drees J R Ellis and C E M Wagner Comput Phys Commun 156 2004 283 arXiv hep ph 0307377 27 28 29 30 J S Lee M Carena J Ellis A Pilaftsis and C E M Wagner Comput Phys Commun 180 2009 312 arXiv 0712 2360 hep ph J S Lee A Pilaftsis M Carena S Y Choi M Drees J Ellis C Wagner http www hep man ac uk u jslee CPsuperH html U Ellwanger J Gunion C Hugonie http www th u psud fr NMHDECAY nmssmtools html W H Press S A Teukolsky W T Vetterling and B P Flannery Numerical R
47. ring OM MUNCIE sir e 2 Aa oi 8 we ak ae Se a Oe aed ew e i 7 3 Auxiliary routines ob 2 Gia we Bae He Bod Se oe Oe ve FS Indirect detection 8 1 Interpolation and display of spectra 42 6605 4 4 04 44444 44 8 2 Annihilation spectra 64 4 ose ed ae got es we OE ORR Oe A OG 8 3 Distribution of Dark Matter in Galaxy 1 244 lt 4 48 eG4e 8 eo oa Photon signal os s s toe groe crated aca eS OES a ee Be ee Ook So Propagation of charged particles o oaa a a 8 6 Experimental data and backgrounds aooo a a 254 eee aos 1 9 Neutrino signal from the Sun and the Earth 10 Cross sections and decays 11 Tools for model independent analysis 12 Additional routines for specific models 1 MoM ee ake eek a eS ee ee ee ee ee eae ee ee a 12 2 The NMSSM eee naona ere be one SE OS Ss ee ee ee 12 3 The CPVMSSM 25 4 Ses Bo G ee eo ee ee See Be ERS AS a 13 Tools for new model implementation Devel VIR steps ri aene oF die he Se ww Re ee he ee ed 13 2 Automatic width calculation lt 46 s aa6 5 68 hd bee hee od 13 3 Using LanHEP for model file generation 134 QCD f nctions sse re BAe ee BS be be ee oe eee 88 13 5 SLHA reader s soeg so ere he eek oe BS Re OES eee Oe RS 13 5 1 Writing an SLHA input file 4 i04 6 044468 44 4 4 1 13 6 Routines for diagonalisation 4 2G 4 wb Ee ik ee a are ww 14 Mathematical tools A An updated routine for b sy in the MSSM B Solution of equation for reli
48. rn the same result even if the user has changed the VW VZdecay switch We recommend to call ecleanDecayTable after changing the switches to force micrOMEGAs to recalculate the widths taking into account the new value of VW VZdecay In Fortran the subroutine e setVVdecay VWdecay VZdecay changes the switches and calls cleanDecayTable The sortOddParticles command which must be used to recompute the particle spec trum after changing the model parameters also clears the decay table If the particle widths were stored in the SLHA file Susy Les Houches Accord 18 downloaded by micrOMEGAs then the SLHA value will be used by and are thus insen sitive to the VW VZdecay switches To avoid downloading particle widths one can use slhaRead fileName mode 4 to read the content of the SLHA file see the description in Section 13 5 The temperature dependence of the effective number of degrees of freedom can be set with e loadHeffGeff char fname allows to modify the temperature dependence of the effective number of degrees of freedom by loading the file fname which contains a table of hers T gefp T A positive return value corresponds to the number of lines in the table A negative return value indicates the line which creates a problem e g wrong format the routine returns zero when the file fname cannot be opened The default file is std_thg tab and is downloaded automatically if loadHeffGeff is not called is user s main program Five oth
49. rth fa ss dv exp See d v v V o lt Umax which corresponds to the isothermal model Default values for the global parameters Av Vrot Umaz Vesc Vearth are listed in Table 1 Cyorm is the normalization factor This function is an argument of the nucleusRecoil function described above e nucleusRecoil0 f A Z J Sp Sn qBOX dNdE is similar to the function nucleusRecoil except that the spin dependent nuclei form factors are described by Gauss functions whose values at zero momentum transfer are defined by the coefficients Sp Sn 4 Predefined values for the coefficients Sp Sn are included for the nuclei listed in nucleusrecoil as well as He C s Their names are Sp_ Nucleus Name Atomic Number Sn Nucleus Name Atomic Number One can use this routine for nuclei whose form factors are not known 7 3 Auxiliary routines Two auxiliary routines are provided to work with the energy spectrum computed with nucleusRecoil and nucleusRecoil0 e cutRecoilResult dNdE E1 E2 calculates the number of events in an energy interval defined by the values E1 E2 in keV e displayRecoilPlot dNdE title E1 E2 plots the generated energy distribution dNdE Here title is a character string specifying the title of the plot and E1 E2 are minimal and maximal values for the displayed energy in keV 8 Indirect detection 8 1 Interpolation and display of spectra Various spectra and fluxes of particles relevant for indirect d
50. ry quantum numbers 3 Downloading and compilation of micrOMEGAs To download micrOMEGAs go to http lapth cnrs fr micromegas and unpack the file received micromegas_4 0 tgz with the command tar xvzf micromegas_4 0 tgz This should create the directory micromegas_4 0 which occupies about 40 Mb of disk space You will need more disk space after compilation of specific models and generation of matrix elements In case of problems and questions email micromegas lapth cnrs fr 3 1 File structure of micrOMEGAsS Makefile to compile the kernel of the package CalcHEP_src generator of matrix elements for micrOMEGAs Packages external codes clean to remove compiled files man contains the manual description of micrOMEGAs routines newProject to create a new model directory structure sources micrOMEGAs code MSSM model directory MSSM Makefile to compile the code and executable for this model main c pp main F files with sample main programs lib directory for routines specific to this model Makefile to compile the auxiliary code library lib aLib a c f source codes of auxiliary functions work CalcHEP working directory for the generation of matrix elements Makefile to compile the library work work_auz a models directory for files which specifies the model vars1 mdl free variables funci mdl constrained variables prtcls1 mdl particles lgrngi mdl Feynman rules tmp auxiliary directories for CalcHEP sessions re So sults
51. s NMSPEC 23 in the NMSSMTools_4 0 pack age 29 e nmssmEWSB void calculates the masses of Higgs and supersymmetric particles in the NMSSM starting from the weak scale input parameters These can be downloaded by the readVarNMSSM rou tine 24 e nmssmSUGRA m0 mhf a0 tb sgn Lambda aLambda aKappa calculates the parameters of the NMSSM starting from the input parameters of the CNMSSM The routines for computing constraints are taken from NMSSMTools see details in 3 e bsgnlo amp M amp P bsmumu amp M amp P btaunu amp M amp P gmuon amp M amp P are the same as in the MSSM case Here the output parameters M and P give information on the lower upper experimental limits 25 e deltaMd deltaMs compute the supersymmetric contribution to the Bis B mass differences AM4 and AM e NMHwarn FD is similar to masslimits_ except that it also checks the constraints on the Higgs masses returns the number of warnings and writes down warnings in the file FD e loopGamma amp vcs_gz kvcs_gg calculates ov for loop induced processes of neutralino annihilation into yZ and into yy 3 The result is given in gt In case of a problem the function returns a non zero value 12 3 The CPVMSSM The independent parameters of the model include in addition to some standard model parameters only the weak scale soft SUSY parameters The independent parameters are listed in CPVMSSM work models varsi mdl Masses m
52. s are stored in nu and nu_bar arrays of dimension NZ 250 The neutrino fluxes are expressed in 1 Year km The function SpectdNdE E nu returns the differential flux of neutrinos in 1 Year km GeV and displaySpectrum nu nu from Sun 1 Year km 2 GeV Emin Emax 1 allows to display the corresponding spectrum on the screen e muonUpward nu Nu rho muon calculates the muon flux which results from interactions of neutrinos with rocks below the detector Here nu and Nu are input arrays containing the neutrino anti neutrino fluxes calculated by neutrinoFlux rho is the Earth density 2 6g cm muon is an array which stores the resulting sum of u u fluxes SpectdNdE E muon gives the differential muon flux in 1 Year km GeV units e muonContained nu Nu rho muon calculates the flux of muons produced in a given detector volume This function has the same parameters as muonUpward except that the outgoing array gives the differential muon flux resulting from neutrinos converted to muons 20 in a km volume given in 1 Year km GeV units rho is the density of the detector in g cm Two functions allow to estimate the background from atmospheric neutrinos creating muons after interaction with rocks below the detector or with water inside the detector e ATMmuonUpward cosFi E calculates the sum of muon and anti muon fluxes resulting from the interaction of atmospheric neutrinos with rocks in units of 1 Year km GeV Sr cosFi is the energy
53. s in the SLHA format Such routines can be very useful for the implementation of new models In general a SLHA file contains several pieces of information which are called blocks A block is characterized by its name and sometimes by its energy scale Each block contains the values of several physical parameters characterized by a key The key consists in a sequence of integer numbers For example 29 BLOCK MASS Mass spectrum PDG Code mass particle 25 1 15137179E 02 lightest neutral scalar 37 1 48428409E 03 charged Higgs BLOCK NMIX Neutralino Mixing Matrix 1 1 9 98499129E 01 Zni1 1 2 1 54392008E 02 Zn12 BLOCK Au Q 4 42653237E 02 The trilinear couplings 1 14 8 22783075E O2 A_u Q DRbar 2 2 8 22783075E 02 A_c Q DRbar e slhaRead filename mode downloads all or part of the data from the file filename mode is an integer which determines which part of the data should be read form the file mode 1 m1 2 m2 4 m4 where mi 0 1 overwrites all keeps old data m2 0 1 reads DECAY does not read DECAY m4 0 1 reads BLOCK does not read BLOCK For example mode 2 m1 0 m2 1 is an instruction to overwrite all previous data and read only the information stored in the BLOCK sections of filename In the same manner mode 3 is an instruction to add information from DECAY to the data obtained previously slhaRead returns the values O successful reading 1 can not open the file 2 error in spectrum calcula
54. sForSh into FlagsForMake and substitutes its contents in all Makefiles of the package g m g m ake clean deletes all generated files but asks permission to delete FlagsForSh ake flags only generates FlagsForSh It allows to check and change flags before compilation of codes 3 3 Module structure of main programs Each model included in micrOMEGAs is accompanied with sample files for C and Fortran programs which call micrOMEGAs routines the main c main F files These files consist of several modules enclosed between the instructions ifdef XXXXX endif Each of these blocks contains some code for a specific problem define MASSES_INFO Displays information about mass spectrum define CONSTRAINTS Displays B_ gt sgamma Bs gt mumu etc define OMEGA Calculates the relic density define INDIRECT_DETECTION Signals of DM annihilation in galactic halo define LoopGAMMA Gamma Ray lines available only in some models define RESET_FORMFACTORS Redefinition of Form Factors and other parameters define CDM_NUCLEON Calculates amplitudes and cross sections for DM nucleon collisions define CDM_NUCLEUS Calculates number of events for 1kg day and recoil energy distribution for various nuclei define NEUTRINO Calculates flux of solar neutrinos and the corresponding muon flux define DECAYS Calculates decay widths and branching ratios define CROSS_SECTIONS Calculates cross sections define CLEAN Removes int
55. set the polarization of the initial massless beam define Helicity i where i 0 1 for the 1 and 2 particles respectively The helicity is defined as the projection of the particle spin on the direction of motion It ranges from 1 1 for spin 1 particles and from 0 5 0 5 for spin 1 2 particles By definition a left handed particle has a positive helicity e hCollider Pcm pp pName1 pName2 calculates the cross section for particle production at hadron colliders Here Pcm is the beam energy in the center of mass frame pp is 1 1 for pp pp collisions pName1 and pName2 are the names of outgoing particles The value returned is the cross section in pb The QCD scale is fixed to Q m pNamel m pName2 2 11 Tools for model independent analysis A model independent calculation of the DM observables is also available After specifying the DM mass the cross sections for DM spin dependent and spin independent scatter ing on proton and neutron the DM annihilation cross section times velocity at rest and the relative contribution of each annihilation channel to the total DM annihilation cross section one can compute the direct detection rate on various nuclei the fluxes for pho tons neutrinos and antimatter resulting from DM annihilation in the galaxy and the neutrino muon fluxes in neutrino telescopes 3In Fortran the format is call newProcess procName address 22 e nucleusRecoilAux f A Z J Sxx csIp csIn csDp csDn dNdE
56. t is Xtot 2 e vSigmaCh is an array that contains the relative contribution and particle names for each annihilation channel It is similar to vSigmaTCh described above but list of particle has 5 positions to describe gamma radiation For 2 gt 2 processes vSigmaCh n prtcl 4 NULL The array vSigmaCh is filled by calcSpectrum In the Fortran version one uses instead the function vSigmaCh i weight pdg process which also is similar to Fortran vSigmaTCh described above 17 8 3 Distribution of Dark Matter in Galaxy The indirect DM detection signals depend on the DM density in our Galaxy The DM density is given as the product of the local density at the Sun with the halo profile function A T Po Fhaio r 4 In micrOMEGAs p is a global parameter rhoDM and the Zhao profile 12 Ro re R3 Fhaio r 55 5 with a 1 8 3 y 1 rc 20 kpc is used by default Ro the distance from the Sun to the galactic center is also a global parameter Rsun The parameters of the Zhao profile can be reset by e setProfileZhao a 7 rc The function to set another density profile is e setHaloProfile Fhaio r where Fhaio r is any function which depends on the distance from the galactic center r defined in kpc units For instance setHaloProfile hProfileEinasto sets Einasto profile Fhato r exp ei 7 where by default a 0 17 but can be changed by e setProfileEinasto a The command setHaloProfile hProfileZha
57. t valid for Mcdm lt 2GeV as explained in the description of calcSpectrum e captureAux f forSun csIp csIn csDp csDn calculates the number of DM particles captured per second assuming the cross sections for spin independent and spin dependent interactions with protons and neutrons csIp csIn csDp csDn are given as input parameters in pb A negative value for one of the cross sections is interpreted as a destructive interference between the proton and neu tron amplitudes The first two parameters have the same meaning as in the neutrinoFlux routine Section 9 The result depends implicitly on the global parameters rhoDM and Mcdm in Table 1 e basicNuSpectra forSun pdgN outN nu calculates the v and v spectra corresponding to DM annihilating into particles specified by the PDG code pdgN Effects of interaction with Sun Earth medium as well as neutrino oscillation are taken into account 39 outN should be chosen 1 for muon neutrino and 1 for anti neutrino The resulting spectrum is stored in the array nu with NZ 250 elements which can be checked by the SpectdNdE E nu function The files main c F in the directory mdlIndep contain an example of the calculation of the direct detection indirect detection and neutrino telescope signals using the routines described in this section The numerical input data in this sample file corresponds to MSSM mssmh dat 23 12 Additional routines for specific models The models included in micr
58. the default values for the experimentally determined quantities B B X 7 B B gt X e0 Kyto 6 9 34 B B gt X ev 0 1064 37 Csi 0 546 35 Vis Vio Vool 0 9613 37 A 0 808 0 2253 p 0 132 7 0 341 Ma Ms 50 Ay amp 4 m3 m3 0 12GeV 36 as Mz 0 1189 Table 4 Default values in micrOMEGAs in Eq 9 see Table A and we have replaced the factor f zo by Cs where Vab Vo T B Xer T B Xen Cy 10 accounts for the me dependence in B gt Xen The CKM matrix elements in the Wolfenstein parametrisation given in Table A are used to compute the central value of ckmf at order A V Va cb ckmf 1 A 27 1 AP 7 A 11 With these default values the NLO improved SM contribution is B B gt X 7 sm 3 27 x 1074 which corresponds to the result of Gambino and Giordano 35 after correcting for the slightly different CKM parameter used ckm f 0 963 We have performed a comparison with superIso3 1 which includes the NNLO SM calculation for 10 randomly generated MSSM scenarios The results are presented in Fig A after applying a correction factor in superISO to account for the different value for the overall factor F B B X ev Or The ratio of Finicro Fiso 0 942 The two codes agree within 5 most of the fra B Solution of equation for relic density in case of 2 DM components In terms of AY Y
59. tion of the W Z bosons key 1 or photon radiation key 2 Note that final state photon radiation FSR is always included When key 2 the 3 body process yy XX 7 is computed for those subprocesses which either contain a light particle in the t channel of mass less than 1 2 Mcdm or an outgoing W when Mcdm gt 500GeV The FSR is then subtracted to avoid double counting Only the electron positron spectrum is modified with this switch When key 4 the contibutions for each channel to total annihilation rate are written on the screen More than one option can be switched on simultaneously by adding the corresponding values for key For example both the W polarization and photon radiation effects are included if key 3 A problem in the spectrum calculation will produce a non zero error code err 0 calcSpectrum interpolates and sums spectra obtained by Pythia The spectra tables are provided only for Mcdm gt 2GeV The results for a dark matter mass below 2 GeV will therefore be wrong for example an antiproton spectrum with kinematically forbidden energies will be produced A warning is issued for Mcdm lt 2GeV e spectrInfo Xmin spectrTab amp Ntot amp Xtot provides information on the spectra generated Here Xmin defines the minimum cut for the energy fraction x E Mcdm Ntot and Xtot are calculated parameters which give on average the total number and the energy fraction of the final particles produced per collision Note that the upper limi
60. tor 3 no data n gt 0 wrong file format at line n e slhaValExists BlockName keylength keyl key2 checks the existence of specific data in a given block BlockName can be substituted with any case spelling The keylength parameter defines the length of the key set key1 key2 For example slhaValExists Nmix 2 1 2 will return 1 if the neu tralino mass mixing element Zn12 is given in the file and 0 otherwise e slhaVal BlockName Q keylength key1 key2 is the main routine which allows to extract the numerical values of parameters BlockName and keylength are defined above The parameter Q defines the scale dependence This parameter is relevant only for the blocks that contain scale dependent parameters it will be ignored for other blocks for example those that give the particle pole masses In general a SLHA file can contain several blocks with the same name but different scales the scale is specified after the name of the block slhaVal uses the following algorithm to read the scale dependent parameters If Q is less greater than all the scales used in the different blocks for a given parameter slhaVal returns the value corresponding to the minimum maximum scale contained in the file Otherwise slhaVal reads the values corresponding to the two scales Q and Q just below and above Q and performs a linear interpolation with respect to log Q to evaluate the returned values 30 Recently it was proposed to use an
61. tron spectrum after propagation Emin is the energy cut to be defined by the user Note that a low value for Emin increases the computation time The format is the same as for the initial spectrum The function SpectrdNdE E Sobs described above can also be used for the interpolation in this case the flux is returned in GeV s cm sr 71 e pbarFlux E dSigmavdE computes the antiproton flux for a given energy E and a differential cross section for antiproton production dSigmavdE For example one can substitute dSigmavdE ovSpectdNdE E SpP where ov and SpP are obtained by calcSpectrum This function does not depend on the details of the particle physics model and allows to analyse the dependence on the parameters of the propagation model e pbarFluxTab Emin sigmav Sp Sobs computes the antiproton flux this function works like posiFluxTab e solarModulation Phi mass stellarTab earthTab takes into account modification of the interstellar positron antiproton flux caused by the electro magnetic fields in the solar system Here Phi is the effective Fisk potential in 19 MeV mass is the particle mass stellarTab describes the interstellar flux earthTab is the calculated particle flux in the Earth orbit Note that for solarModulation and for all FluxTab routines one can use the same array for the spectrum before and after propagation 8 6 Experimental data and backgrounds Background for anti proton signal is caused by collision of pr
62. uation and increases the number of function calls in the regions where the integrand has peaks e gauss F x1 x2 N performs Gauss N point integration for N lt 8 33 e odeint Y Dim x1 x2 eps hi deriv solves a system of Dim differential equations in the interval x1 x2 The array Y contains the starting variables at x1 as an input and is replaced by the resulting values at x2 as an output eps determines the precision of the calculation and h1 gives an estimation of step of calculation The function deriv calculates Y dY dx with the call deriv x Y Y The Runge Kutta method is used see details in 30 e buildInterpolation F x1 x2 eps amp Dim amp X amp Y constructs a cubic interpolation of the function F in the interval x1 x2 eps controls the precision of interpolation If eps lt 0 the absolute precision is fixed otherwise a relative precision is required The function checks that after removing any grid point the function at that point can be reproduced with a precision eps using only the other points It means that the expected precision of interpolation is about eps 16 Dim gives the number of points in the constructed grid X and Y are variables of the double type The function allocates memory for Dim array for each of these parameters Xi contains the x grid while Y i F X i e polint4 x Dim X Y performs cubic interpolation for Dim dimension arrays X Y A similar function polint3 performs quadratic
63. udjema A Pukhov and A Semenov Comput Phys Commun 174 2006 577 arXiv hep ph 0405253 co G Belanger F Boudjema A Pukhov and A Semenov Comput Phys Commun 176 2007 367 arXiv hep ph 0607059 ns G Belanger F Boudjema A Pukhov and A Semenov Comput Phys Commun 180 2009 747 arXiv 0803 2360 hep ph OU G Belanger F Boudjema P Brun A Pukhov S Rosier Lees P Salati and A Se menov arXiv 1004 1092 hep ph D G Belanger F Boudjema A Pukhov and A Semenov arXiv 1305 0237 hep ph 7 A Belyaev C R Chen K Tobe and C P Yuan Phys Rev D 74 2006 115020 hep ph 0609179 8 R Barbieri L J Hall and V S Rychkov Phys Rev D 74 2006 015007 hep ph 0603188 Ke G Belanger K Kannike A Pukhov and M Raidal JCAP 1204 2012 010 arXiv 1202 2962 hep ph 10 M Hindmarsh and O Philipsen Phys Rev D 71 2005 087302 hep ph 0501232 37 11 0 12 13 14 15 16 17 J Beringer et al Particle Data Group Collaboration Phys Rev D 86 2012 10001 H Zhao Mon Not Roy Astron Soc 278 1996 488 astro ph 9509122 J Lavalle J Pochon P Salati and R Taillet Astron Astrophys 462 2007 827 astro ph 0603796 B Allanach et al Comput Phys Commun 180 2009 8 arXiv 0801 0045 hep ph C Hugonie G Belanger and A Pukhov JCAP 0711 2007 009 arXiv 0707 0628 hep ph G Belange
64. uture The returned parameter address gives an address where information about the decay channels is stored In C the address should be of type txtList For models which read a SLHA parameter file the values of the widths and branchings are taken from the SLHA file unless the user chooses not to read this data see Section 13 5 for details e printTxtList address FD lists the decays and their branching fractions and writes them in a file address is the address returned by pWidth e findBr address pattern finds the branching fraction for a specific decay channel specified in pattern a string containing the particle names in the CalcHEP notation The names are separated by commas or spaces and can be specified in any order e slhaDecayPrint pname FD uses pWidth described above to calculate the width and branching ratios of particle pname and writes down the result in SLHA format The return value is the PDG particles code In case of problem for instance wrong particle names this function returns zero This function first tries to calculate 1 2 decays If such decays are kinematically forbidden 21 then 1 3 decay channels are computed e newProcess procName compiles the codes for any 2 2 or 1 2 reaction The result of the compilation is stored in the shared library in the directory work so generated The name of the library is generated automatically The newProcess routine returns the address of the compile

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