micrOMEGAs is a tool for cold dark matter (DM) studies in generic extensions
of the standard model with a R-parity like discrete symmetry that guarantees
the stability of the lightest odd particle. The code computes the DM relic
density, the elastic scattering cross sections of DM on nuclei relevant for
direct detection, and the spectra of positrons, anti-protons and photons
originating from DM annihilation including porpagation of charged cosmic rays.
The cross sections and decay properties of new particles relevant for collider
studies are included as well as constraints from the flavour sector on the
parameter space of supersymmetric models.Comment: 10 pages, Proceedings of LC09, e+e- Physics at the TeV scale and the
  Dark Matter connection, Perugia, Italy, 21-24 sept. 200

Belanger, G.

Boudjema, F.

Pukhov, A.

Semenov, A.

English

arXiv

micrOMEGAs is a tool for cold dark matter (DM) studies in generic extensions of the standard model with a R-parity like discrete symmetry that guarantees the stability of the lightest odd particle. The code computes the DM relic

density, the elastic scattering cross-sections of DM on nuclei relevant for direct detection, and the spectra of e+, ¯p, γ originating from DM annihilation including

propagation of charged cosmic rays. The cross-sections and decay properties of new particles relevant for collider studies are included as well as constraints from the

flavour sector on the parameter space of supersymmetric models

Bélanger, G.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10591-3Colloquia: LC09IL NUOVO CIMENTO Vol. 33 C, N. 2 Marzo-Aprile 2010micrOMEGAs: A tool for dark matter studiesG. Be´langer(1), F. Boudjema(1), A. Pukhov(2) and A. Semenov(3)(1) LAPTH, Universite´ de Savoie, CNRS - B.P.110, F-74941 Annecy-le-Vieux, France(2) Skobeltsyn Institute of Nuclear Physics, Moscow State UniversityMoscow 119992, Russia(3) Joint Institute of Nuclear Research (JINR) - 141980, Dubna, Russia(ricevuto il 15 Febbraio 2010; approvato il 23 Marzo 2010; pubblicato online il 21 Maggio 2010)Summary. — micrOMEGAs is a tool for cold dark matter (DM) studies in genericextensions of the standard model with a R-parity like discrete symmetry that guar-antees the stability of the lightest odd particle. The code computes the DM relicdensity, the elastic scattering cross-sections of DM on nuclei relevant for direct de-tection, and the spectra of e+, p¯, γ originating from DM annihilation includingpropagation of charged cosmic rays. The cross-sections and decay properties of newparticles relevant for collider studies are included as well as constraints from theflavour sector on the parameter space of supersymmetric models.PACS 12.60.-i – Models beyond the standard model.PACS 95.35.+d – Dark matter (stellar, interstellar, galactic, and cosmological).1. – IntroductionThe existence of a dominant dark matter component in the universe has been firmlyestablished by cosmological observations in the last few years notably by SDSS [1] andWMAP [2]. Furthermore, the amount of DM today, the relic density, has been measuredwith very good precision, Ωh2 = 0.1099± 0.0062 [3]. A leading candidate for cold DM isa new weakly interacting stable massive particle which naturally provides a reasonablevalue for the relic density. It is particulary interesting that extensions of the standardmodel (SM) whose prime goal is to solve the hierarchy problem can in many cases alsoprovide a viable DM candidate. Such particles arise naturally in many extensions of thestandard model [4] from the minimal supersymmetric standard model [5, 6] to modelsof extra dimensions [7, 8], little Higgs models [9] or models with extended gauge orHiggs sectors [10, 11]. In these models which possess a symmetry like R-parity thatguarantees the stability of the lightest odd particle (LOP), the DM candidate can beeither a Majorana fermion, a Dirac fermion, a vector boson or a scalar. The DM massranges anywhere from a few GeV’s to a few TeV’s.c© Societa` Italiana di Fisica 111112 G. BE´LANGER, F. BOUDJEMA, A. PUKHOV and A. SEMENOVAstroparticle and collider experiments are being actively pursued to search for DM.Combined studies of DM signals in these different types of experiments should providethe necessary ingredients to unravel the nature of DM. These involve searches for DMeither directly through detection of elastic scattering of the DM with the nuclei in alarge detector or indirectly trough detection of products of DM annihilation (photons,positrons, neutrinos or antiprotons) in the Galaxy or in the Sun. Furthermore collidersare searching for DM as well as for other new particles predicted in extensions of thestandard model.Sophisticated tools have been developed to perform computations of DM observ-ables within R-parity conserving supersymmetric models, four are publicly available:micrOMEGAs [12], DarkSUSY [13], IsaTools [14] and superISO [15]. All include precisecomputations of the relic density as well as various constraints on the model from pre-cision observables or the flavour sector. In addition the first three compute the directand indirect detection rates while micrOMEGAs and Isatools provide collider observ-ables. micrOMEGAs has the added important feature that it can be easily generalised toother extensions of the standard model [16]. This is because micrOMEGAs is structuredaround CalcHEP [17] a generic program which once given a model file containing the listof particles, their masses and the associated Feynman rules describing their interactions,computes any cross-section in the model. The standard micrOMEGAs routines can thenbe used to compute the relic density as well as other DM observables.2. – Relic densityA relic density calculation entails solving the evolution equation for the abundance ofDM, Y (T ), defined as the number density divided by the entropy density [18],(1)dYdT=√πg∗(T )45Mp〈σv〉(Y (T )2 − Yeq(T )2),where g∗ is an effective number of degree of freedom, Mp is the Planck mass and Yeq(T )the thermal equilibrium abundance. 〈σv〉 is the relativistic thermally averaged annihila-tion cross-section. The dependence on the specific particle physics model enters only inthis cross-section which includes all annihilation and coannihilation channels,(2) 〈σv〉 =∑i,j gigj∫(mi+mj)2ds√sK1(√s/T )p2ij∑k,l σij;kl(s)2T (∑i gim2iK2(mi/T ))2 ,where gi is the number of degree of freedom, σij;kl the total cross-section for annihilationof a pair of odd particles with masses mi, mj into some Standard Model particles (k, l),and pij(√s) is the momentum (total energy) of the incoming particles in their center-of-mass frame.Integrating eq. (1) from T =∞ to T = T0 leads to the present day abundance Y (T0)needed in the estimation of the relic density,(3) ΩLOPh2 =8π3s(T0)M2p (100 (km/s/Mpc))2MLOPY (T0) = 2.742× 108MLOPGeV Y (T0),where s(T0) is the entropy density at present time and h the normalized Hubble constant.MICROMEGAS: A TOOL FOR DARK MATTER STUDIES 113To compute the relic density, micrOMEGAs solves the equation for the abundanceeq. (1), numerically without any approximation. The computation of all annihilationand coannihilation cross-sections are done exactly at tree-level. For this we rely onCalcHEP [17]. In the thermally averaged cross-section, eq. (2), coannihilation channelsare compiled and added only when necessary, that is when the mass difference with theLOP does not exceed a value determined by the user.3. – New modelsmicrOMEGAs was first developed for the minimal supersymmetric standard model(MSSM). In this model the large number of annihilation channels made automationdesirable. For this reason micrOMEGAs was based on CalcHEP [17]. The generalisation toother particle physics models was then straigthforward and only requires specifying thenew model file into CalcHEP [17].In order that the program finds the list of processes that need to be computed for thethermally averaged annihilation cross-section, relevant for the relic density calculation,one needs to specify the analogous of R-parity and assign a parity odd or even to everyparticle in the model. The standard model particles have an even parity. The lightestodd particle will then be identified with the DM candidate. micrOMEGAs automaticallygenerates all processes of the type χiχj → X,Y where χi designates all R-parity oddparticle and X, Y all R-parity even particles. micrOMEGAs then looks for s-channel polesas well as for thresholds to adapt the integration routines for higher accuracies in thesespecific regions, and performs the relic density calculation. Note that the code can alsocompute the relic density of a charged particle, this quantity can for example be used toextract the relic density of the gravitino DM.Our approach is very general and, as long as one sticks to tree-level masses and cross-sections, necessitates minimal work from the user beyond the definition of the modelfile. However it has been demonstrated that for an accurate relic density calculation itis necessary in many cases to take into account higher-order corrections. In particularcorrections to the mass of either the LOP or of any particle that can appear in s-channelare important, for example the corrections to Higgs masses in the MSSM or its extensions.The large QCD corrections to the Higgs width must also be taken into account whenannihilation occurs near a Higgs resonance. In general one expects that these loopcorrections can be implemented via an effective Lagrangian. In practice then it mightbe necessary for the user to implement additional routines or interface other programsto take these effects into account. This was done explicitly for the NMSSM [19], theCPVMSSM [20] and the MSSM with Dirac gaugino masses [21].Another advantage of our approach based on a generic program like CalcHEP is thatone can compute in addition any cross-section or decay width in the new model con-sidered. In particular, tree-level cross-sections for 2 → 2 processes and decay widths ofparticles are available. Furthermore the cross-sections times relative velocity, σv, for DMannihilation at v → 0 and the yields for the continuum γ, e+, p¯, ν spectra, relevant forindirect detection of DM, are also automatically computed. The procedure to extractthe elastic scattering cross-section is described next.4. – Direct detectionIn direct detection, one measures the recoil energy deposited by the scattering of DM(χ) with the nuclei. Generically DM-nuclei interactions can be split into spin-independent114 G. BE´LANGER, F. BOUDJEMA, A. PUKHOV and A. SEMENOV(scalar) and spin-dependent interations. The scalar interactions add coherently in thenucleus so heavy nuclei offer the best sensitivity. On the other hand, spin-dependentinteractions rely mainly on one unpaired nucleon and therefore dominate over scalarinteractions only for light nuclei unless scalar interactions are themselves suppressed.In both cases, the cross-section for the DM nuclei interaction is typically low, so largedetectors are required. Many experiments involving a variety of nuclei have been set up.The best limit for spin-independent interactions was reported recently by CDMS withσSIχp ≈ 3.8 × 10−8 pb for a DM mass around 70GeV [22]. This limit already probes afraction of the parameter space of DM models.Many ingredients enter the calculation of the direct detection rate and cover bothastroparticle, particle and nuclear physics aspects. The detection rate depends on theχ-nucleus cross-section which is derived from the interaction at the quark level. Thedifferent matrix elements for χq interactions have to be converted into effective couplingsof DMs to protons and nucleons, this is done through coefficients that describe thequark content in the nucleons. Note that the DM have small velocities, therefore themomentum transfer is very small as compared to the masses of the DM and/or nucleiand the χ-nucleon elastic cross-sections can be calculated in the limit of zero momentumtransfer.The distribution of the number of events over the recoil energy for spin-independentinteractions readsdNSIdE=2Mdettπρ0MχF 2A(q)(λpZ + λn(A− Z))2I(E),(4)where ρ0 is the DM density near the Earth, Mdet the mass of the detector, t the exposuretime, I(E) is an integral over the velocity distribution and FA(q) is the nucleus form factorwhich depends on the momentum transfer. The coefficients λp, λn contain all particlephysics dependence and are extracted from the matrix elements for χq scattering coupledwith coefficients that describe the quark content in the nucleons.Traditionally the coefficients λq of the low-energy effective χq Lagrangian are eval-uated symbolically using Fiertz identities. Instead in micrOMEGAs we use an originalapproach that allows to handle a generic model. First we expand the χq interactionsover a set of basic point-like operators, only a few operators are necessary in the q2 → 0limit. The same operators also describe the DM-nucleon interactions. For example forSI interactions of a Majorana fermion with quarks or nucleons the effective Lagrangianreads(5) LSI = λqψχψχψqψq;micrOMEGAs creates automatically a new model file that contains these operators as newauxiliary vertices in the model. CalcHEP then generates and calculates symbolically alldiagrams for DM-quark/anti-quark elastic scattering at zero momentum transfer. Theinterference terms between one normal vertex and one auxiliary vertex allow to evaluatenumerically the λq coefficients [23]. Note that in the file that defines the model all quarksshould be defined as massive particles. Vertices that depend on light quark masses, forexample the couplings of Higgs to light quarks cannot be neglected. The dominant termfor DM quark scalar interactions is proportional to quark masses, when converting toDM nucleon interactions this quark mass will get replaced by a nucleon mass.MICROMEGAS: A TOOL FOR DARK MATTER STUDIES 1155. – Indirect detectionDM annihilation in the Galactic halo produces pairs of standard model particles.These particle then hadronize and decay into stable particles that evolve freely in theinterstellar medium. The final states with γ, e+, p¯ and D¯ are particularly interesting asthey are the subject of indirect searches. Recently many new results from indirect DMsearches have been released notably by PAMELA and Fermi [24, 25]. The rate for theproduction of these particles can be cast into(6) Q(x, E) =12〈σv〉(ρ(x)mχ)2 dNdE,where 〈σv〉 is the annihilation cross-section times the relative velocity of incoming DMparticles in the zero velocity limit. mχ is the mass of the DM candidate, ρ(x) is the DMdensity at the location x and dN/dE is the energy distribution of the particle producedin one collision. The predictions for the energy spectra depend on non-perturbativeQCD and imply the use of Monte Carlo simulations such as PYTHIA. The annihilationrates are extracted from CalcHEP in any model. The rate for photons observed nearthe center of the galaxy shows a strong dependence on the halo profile in particular onthe DM density near the center, a quantity that still has large uncertainties. Differenthalo profiles are implemented in micrOMEGAs. In addition micrOMEGAs provides, in theMSSM, the rate for gamma-rays that come from direct annihilation of DM particles. Thismodel-dependent process is loop-induced and suppressed but is nevertheless interestingbecause of the dramatic signature, a monochromatic gamma-ray line [26].The charged particles generated from DM annihilation propagate through the Galac-tic halo and their energy spectrum at the Earth differs from the one produced at thesource. Charged particles are deflected by the irregularities of the galactic magnetic field,suffer energy losses from synchroton radiation and inverse Compton scattering as wellas diffusive reacceleration in the disk. Finally galactic convection wipes away chargedparticles from the disk. Solar modulation can also affect the low energy part of thespectrum. The equation that describes the evolution of the energy distribution for allparticles (protons, anti-protons, positrons) reads(7)∂∂z(VCψ)−∇ · (K(E)∇ψ) + ∂∂E(b(E)ψ) = Q(x, E),where ψ = dn/dE is the number density of particles per unit volume and energy. Qis the production rate of primary particles per unit volume and energy, eq. (6). b(E)is the energy loss rate and K is the space diffusion coefficient, assumed homogeneous,K(E) = K0βRδ where β is the particle velocity and R its rigidity. The propagation equa-tion is solved within a semi-analytical two-zone model. Within this approach the regionof diffusion of cosmic rays is represented by a thick disk of thickness 2L and radius R =20 kpc [27] . The thin galactic disk where primary cosmic rays are accelerated lies in themiddle and has a thickness 2h ≈ 200 pc and radius R. The boundary conditions are suchthat the number density vanishes at z = ±L and at r = ±R. The galactic wind is directedoutward along the z direction so the convective velocity is also vertical and of constantmagnitude VC(z) = VCsign(z). The propagation parameters δ, K0, L, VC are constrainedby the analysis of the boron to carbon ratio, a quantity sensitive to cosmic ray trans-port [27]. Propagation induces large uncertainties in the prediction of the spectrum from116 G. BE´LANGER, F. BOUDJEMA, A. PUKHOV and A. SEMENOVDM annihilation, furthermore extracting a signal from DM annihilation requires a carefulunderstanding of the background as well as of astrophysical sources. Only the DM signalwill be included in the first version of the indirect detection module to be released soon.6. – ConclusionmicrOMEGAs is a comprehensive tool for DM studies in extensions of the SM. Theimplementation of new models and new features are being pursued. One objective is amore precise computation of the relic density. Within the MSSM [28] it was shown thatthe one-loop corrections to the annihilation cross-sections could be sizeable as comparedwith the precision expected from PLANCK measurements. An interface between theloop-improved computations and micrOMEGAs is being worked out.∗ ∗ ∗This work was supported in part by the GDRI-ACPP of CNRS and by the ANRproject ToolsDMColl, BLAN07-2-194882. The work of AP was supported by the Russianfoundation for Basic Research, grants RFBR-08-02-00856-a, RFBR-08-02-92499-a and bya State contract No. 02.740.11.0244.REFERENCES[1] Tegmark M. et al., Phys. Rev. D, 74 (2006) 123507.[2] Spergel D. N. et al., Astrophys. J. Suppl., 170 (2007) 377.[3] Dunkley J. et al. (WMAP Collaboration), Astrophys. J. Suppl., 180 (2009) 306.[4] Bertone G., Hooper D. and Silk J., Phys. Rep., 405 (2005) 279.[5] Goldberg H., Phys. Rev. Lett., 50 (1983) 1419.[6] Ellis J. R. et al., Nucl. Phys. B, 238 (1984) 453.[7] Cheng H.-C., Matchev K. T. and Schmaltz M., Phys. Rev. D, 66 (2002) 036005.[8] Agashe K. and Servant G., Phys. Rev. Lett., 93 (2004) 231805.[9] Hubisz J. and Meade P., Phys. Rev. D, 71 (2005) 035016.[10] McDonald J., Phys. Rev. D, 50 (1994) 3637.[11] Barger V. et al., Phys. Rev. D, 75 (2007) 115002.[12] Be´langer G. et al., Comput. Phys. Commun., 174 (2006) 577.[13] Gondolo P. et al., JCAP, 0407 (2004) 008.[14] Baer H., Balazs C. and Belyaev A., JHEP, 03 (2002) 042.[15] Arbey A. and Mahmoudi F., arXiv:0906.0369 [hep-ph].[16] Belanger G. et al., Comput. Phys. Commun., 176 (2007) 367.[17] Pukhov A., hep-ph/0412191.[18] Gondolo P. and Gelmini G., Nucl. Phys. B, 360 (1991) 145.[19] Belanger G., Boudjema F., Hugonie C., Pukhov A. and Semenov A., JCAP, 0509(2005) 001.[20] Belanger G., Boudjema F., Kraml S., Pukhov A. and Semenov A., Phys. Rev. D,73 (2006) 115007.[21] Belanger G., Benakli K., Goodsell M., Moura C. and Pukhov A., JCAP, 0908(2009) 027.[22] Ahmed Z. et al. (The CDMS-II Collaboration), arXiv:0912.3592 [astro-ph.CO].[23] Belanger G. et al., Comput. Phys. Commun., 180 (2009) 747.[24] Adriani O. et al. (PAMELA Collaboration), Nature, 458 (2009) 607.[25] Abdo A. A. et al. (The Fermi LAT Collaboration), arXiv:0905.0025 [astro-ph.HE].[26] Boudjema F., Semenov A. and Temes D., Phys. Rev. D, 72 (2005) 055024.[27] Maurin D., Donato F., Taillet R. and Salati P., Astrophys. J., 555 (2001) 585.[28] Baro N., Boudjema F. and Semenov A., Phys. Lett. B, 660 (2008) 550.

micrOMEGAs: A tool for dark matter studies

10 pages, Proceedings of LC09, e+e- Physics at the TeV scale and the Dark Matter connection, Perugia, Italy, 21-24 sept. 2009micrOMEGAs is a tool for cold dark matter (DM) studies in generic extensions of the standard model with a R-parity like discrete symmetry that guarantees the stability of the lightest odd particle. The code computes the DM relic density, the elastic scattering cross sections of DM on nuclei relevant for direct detection, and the spectra of positrons, anti-protons and photons originating from DM annihilation including porpagation of charged cosmic rays. The cross sections and decay properties of new particles relevant for collider studies are included as well as constraints from the flavour sector on the parameter space of supersymmetric models

HAL Université de Savoie

micrOMEGAs : a tool for dark matter studies

Hal - Université Grenoble Alpes

http://eprints.bice.rm.cnr.it/16837/1/ncc9600.pdf

micrOMEGAs : a tool for dark matter studies

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository

HAL Université de Savoie

Hal - Université Grenoble Alpes