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micrOMEGAs3.1 : a program for calculating dark matter observables

G. Belanger, F. Boudjema, A. Pukhov, A. Semenov

arXiv:1305.0237v2hep-ph

TL;DR

Dark-matter searches require accurate predictions across relic-density, scattering, annihilation, Higgs, and neutrino observables in varied particle-physics models. micrOMEGAs3.1 broadens the Boltzmann treatment and adds new signal and model-independent modules, with specific approximations and scope limitations documented for neutrino spectra and Higgs QCD corrections.

  • Problem

    Accurately computing diverse dark-matter observables across particle-physics models remains necessary for interpreting current and upcoming experimental data.

  • Method

    The update generalizes relic-density equations for asymmetric dark matter and semi-annihilation, adds virtual-vector and loop-induced processes, and provides Higgs, neutrino-telescope, and model-independent calculation facilities.

  • Results

    The program computes expanded dark-matter signals, including neutrino-telescope fluxes from solar or terrestrial capture and three-body annihilation treatments with benchmark differences below 5%.

  • Takeaways & Limitations

    micrOMEGAs3.1 enables broader comparisons of dark-matter models with direct, indirect, neutrino, Higgs, and collider constraints.

  • Takeaways & Limitations

    The effective-vertex Higgs treatment omits QCD corrections to interference terms and can differ more substantially from HDECAY for heavier MSSM Higgs bosons with strong interference.

Abstract

from arXiv · show

micrOMEGAs is a code to compute dark matter observables in generic extensions of the standard model. This new version of micrOMEGAs is a major update which includes a generalization of the Boltzmann equations to accommodate models with asymmetric dark matter or with semi-annihilation and a first approach to a generalization of the thermodynamics of the Universe in the relic density computation. Furthermore a switch to include virtual vector bosons in the final states in the annihilation cross sections or relic density computations is added. Effective operators to describe loop-induced couplings of Higgses to two-photons or two-gluons are introduced and reduced couplings of the Higgs are provided allowing for a direct comparison with recent LHC results. A module that computes the signature of DM captured in celestial bodies in neutrino telescopes is also provided. Moreover the direct detection module has been improved as concerns the implementation of the strange "content" of the nucleon. New extensions of the standard model are included in the distribution.

1 Introduction

micrOMEGAs3.1 extends a general dark-matter-observable calculator to cover additional cosmologies, signals, Higgs processes, and model-independent analyses. It also adds new models and improves interfaces and selected physics routines for interpreting experimental searches.

  • Motivation: micrOMEGAs computes relic density, nuclear scattering, galactic annihilation signals, and neutrino signals from dark-matter capture in celestial bodies.These observables support comparisons with direct-detection, indirect-detection, neutrino-telescope, collider, and precision-measurement data.
  • Relic-density computation: The update generalizes Boltzmann equations to asymmetric dark matter and semi-annihilation, while incorporating the dark-matter asymmetry into direct and indirect detection rates.It also introduces more general early-Universe thermodynamic inputs through alternative geff(T) and heff(T) tables.
  • New observables and processes: New signal calculations cover three-body processes, loop-induced γγ and γZ0 annihilation in selected supersymmetric models, Higgs loop-induced decays, and neutrinos from capture in the Sun or Earth.Virtual W/Z final states can be included in annihilation and relic-density computations, and Higgs signal strengths can be compared with LHC searches.
  • Models and interfaces: New scalar-dark-matter models include the inert doublet model and a Z3-symmetric model, alongside extended MSSM flavor routines and updated interfaces to external codes.The distribution includes LanHEP source code for new models and updated implementations involving NMSSMTools and spectrum generators.
  • Detection and analysis facilities: The release adds model-independent dark-matter observables, allowing specified masses, scattering cross sections, annihilation rates, and channel fractions to generate multiple detection signals.It also introduces a function for dark-matter clumps and a function defining the strange-quark content of the nucleon.

2 Generalization of the relic density computation

The relic-density computation is generalized beyond the standard symmetric, two-body freeze-out picture to include asymmetric dark matter, semi-annihilation, and selected multi-body final states. The implementation tracks particle–antiparticle abundances and supports off-shell gauge-boson processes, while examples show asymmetry- and threshold-dependent effects on the relic density.

  • Generalized Boltzmann equations: The standard Boltzmann treatment is extended to asymmetric dark matter, semi-annihilation, and selected three-body processes.The code retains the usual electroweak-strength freeze-out assumption while relaxing assumptions about particle–antiparticle symmetry and allowed annihilation channels.
  • Generalized Boltzmann equations: For non-self-conjugate dark matter, separate particle and antiparticle abundances are evolved while their abundance difference remains constant.The total relic density is obtained numerically from the generalized evolution equation for the two components.
  • Asymmetric dark matter: An asymmetry always increases the relic abundance relative to the corresponding symmetric model.In the illustrative Dirac-neutrino model, sufficiently large asymmetry times annihilation rate makes the relic density linearly dependent on ∆Y.
  • Asymmetric dark matter: The illustrative asymmetric-dark-matter model is limited by anomaly cancellation and Higgs invisible-width constraints for light masses.The example would require new quarks to be anomaly free, and light dark-matter masses conflict with LHC bounds.
  • Semi-annihilation: Semi-annihilation can affect relic density while changing the abundance only weakly with α, typically by a few percent.The modified equation is implemented, but asymmetric dark matter and semi-annihilation cannot both be present in a specific model.
  • Three-body processes: Off-shell W/Z final states are incorporated through a switch, and the K-factor approximation differs from complete four-body kinematics by less than 5% at freeze-out in an MSSM benchmark.The procedure reconstructs total cross sections from selected leptonic decays and supports annihilation and coannihilation settings.

3 DM in neutrino telescopes

The neutrino-telescope module models dark matter capture, annihilation, evaporation, and neutrino-to-muon signals from the Sun and Earth. It supports self-conjugate and non-self-conjugate dark matter and connects celestial-body signals to scattering and annihilation processes.

  • Neutrino signals: DM captured in the Sun or Earth annihilates into Standard Model particles whose decays produce neutrinos observable at Earth.The neutrino spectrum depends on the dominant annihilation channel, with direct neutrino production giving the hardest spectrum, followed by muons and W bosons.
  • Experimental relevance: Solar or terrestrial capture signals usually dominate galactic neutrino signals, and IceCube currently provides a strong spin-dependent proton limit.The reported limit is σSD = 1.2×10−40cm−2 for mDM = 200GeV, while Super-Kamiokande is more sensitive for light DM because its threshold is 1.6 GeV.
  • Capture: The capture rate depends on the DM–nucleus scattering cross section, DM velocity distribution, and local density.The calculation includes velocity-dependent scattering and form-factor effects, with coherent spin-independent contributions summed over nuclei and hydrogen providing the largest spin-dependent contribution.
  • Evaporation: Evaporation is important for light DM and typically affects solar DM particles lighter than 3 GeV.The evaporation calculation uses the temperature profile and an integrated scattering cross section inside a radius where the temperature falls to 95% of its mean-radius value.
  • Evolution: The Sun/Earth evolution equations include capture, annihilation, and evaporation, and are solved numerically without assuming equilibrium.For self-conjugate DM, equilibrium makes the annihilation rate depend only on capture; for non-self-conjugate DM, coupled particle and antiparticle equations include distinct capture and annihilation channels.
  • Muon signals: The module converts neutrino spectra into contained and upward muon fluxes using charged-current interactions and muon energy loss during propagation.The neutrino flux includes branching fractions, annihilation spectra, oscillations, and Sun/Earth medium effects; the default neutrino-pair treatment averages over three flavors.

4 Dark matter detection

The detection modules add indirect-signal calculations for loop-induced gamma-ray lines, halo clumping, and direct-detection treatments using updated nucleon inputs. They also extend predictions to dark matter captured in celestial bodies and improve strange-quark-content handling.

  • Indirect detection: The updated detection routines compute loop-induced neutralino annihilation into γγ and γZ in the NMSSM and CPVMSSM.The lGamma.exe routine reads SLHA parameters and returns the corresponding annihilation cross sections.
  • Indirect detection: Halo-clumping functions model enhanced annihilation rates through constant or distance-dependent clump parameters.The simple model uses the clump fraction fcl and clump density ρcl; farther from the Galactic center, the rate can scale as ρ(r) rather than ρ(r)^2.
  • Direct detection: The module accounts for theoretical uncertainty in nucleon quark coefficients, especially the strange-quark content, when computing direct-detection rates.The nucleon-coefficient inputs are organized in the nucleon-coefficients table.
  • Direct detection: Direct-detection calculations replace the earlier σ0-based strange-quark extraction with a more direct σs-based determination from lattice QCD.The weighted mean gives σs = 42 ± 5 MeV and σπN = 34 ± 2 MeV, and calcScalarQuarkFF computes the resulting scalar coefficients.

5 The Higgs sector at colliders

The Higgs-sector update introduces effective loop-induced Higgs couplings to photons and gluons, includes contributions from charged particles and QCD corrections, and provides tools for collider signal-strength comparisons. Its effective-vertex treatment is approximate, with differences from HDECAY generally small for SM-like cases but larger in some heavy-Higgs scenarios.

  • Loop-induced Higgs production and decay: Effective operators extend Higgs production and decay calculations to loop-induced couplings of CP-even and CP-odd Higgs states to photons and gluons.The operators receive contributions from charged scalars, vector bosons, and fermions.
  • Loop-induced Higgs production and decay: The implementation includes loop functions and QCD corrections for fermion, scalar, and vector contributions to effective Hγγ and Hgg vertices.LanHEP can extract the required vertex expressions, including selected tensor structures, real or imaginary parts, and abbreviated forms.
  • Accuracy and limitations: The top contribution to hgg partial widths agrees with the cited reference through order αs^3.The effective-vertex approach incorporates only part of the higher-order corrections and cannot include QCD corrections to interference terms.
  • Accuracy and limitations: For a 126 GeV Standard Model Higgs, differences from HDECAY remain below the percent level, while larger discrepancies occur for heavier MSSM Higgs states with strong top-stop interference.Differences for the SM-like MSSM Higgs are generally at the few-percent level.
  • Higgs signal strengths: The signal-strength machinery compares Higgs production and decay channels with Standard Model expectations using normalized couplings and partial-width ratios.The production-cross-section ratio is approximated by the corresponding partial-width ratio, despite potentially different QCD correction factors.

6 Dark matter models

micrOMEGAs 3.1 expands its model library and updates MSSM/NMSSM support with Higgs, flavor, and effective-vertex features. It also provides model-independent calculations of direct, indirect, and neutrino-telescope dark matter signals.

  • Model distribution: The distribution includes MSSM extensions, LHM, RHNM, IDM, Z3ID, and SM4, with model-independent dark matter calculations also available.All models except SM4 were available in previous versions; effective Higgs vertices and reduced Higgs couplings are included for most models.
  • MSSM updates: The MSSM update adds effective Hgg and Hγγ vertices, tau threshold corrections, an improved Higgs effective potential, and expanded flavor observables.The added flavor observables include K+ →µν and Ds →µν, τν constraints.
  • MSSM updates: The charged-Higgs contribution to kaon leptonic decays is evaluated through a lower-uncertainty quantity whose measured value is Rl23 = 1.004 ± 0.007.Supersymmetric dependence enters through higher-order corrections and can be enhanced by tan β.
  • NMSSM updates: The NMSSM update provides an NMSSMTools 4.0 interface, reduced Higgs couplings, effective Hgg and Hγγ vertices, and an extended Higgs effective potential.The new Higgs self-coupling can in some cases have a large effect on the dark matter relic density.
  • Model-independent observables: The model-independent module computes direct-detection rates, annihilation products, and neutrino-telescope signals from specified masses, scattering cross sections, annihilation rates, and channel contributions.It covers photons, neutrinos, positrons, and antiprotons, including dark matter captured in celestial bodies.

7 External codes in micrOMEGAs

micrOMEGAs 3.1 extends interoperability with external spectrum, flavor, decay, and Higgs-analysis codes through SLHA-based interfaces. SLHAplus also gains flexible parsing for varied block formats and textual records.

  • External packages: micrOMEGAs 3.1 distributes external public codes including SuSpect, CPsuperH, HiggsBounds-4.0.0, and LoopTools-2.1.These codes are compiled when installing a model that requires them or at runtime rather than during the general installation.
  • SLHAplus interface: The SLHAplus package reads blocks with arbitrary formats and adds slhaValFormat for extracting numerical values according to C-style formats.The function can retrieve entries such as neutralino masses and b →sγ branching ratios while respecting scale dependence through Q.
  • SLHAplus interface: SLHAplus supports textual block records through slhaSTRFormat, allowing extraction of channel descriptions from HiggsBounds results.The example identifies the channel with the strongest Higgs constraint.
  • External packages: The interface attaches SOFTSUSY, SPHENO, ISAJET, SuperIso, SUSY-HIT, HDECAY, and SusyBSG to micrOMEGAs.The external packages communicate through SLHA-formatted files, except LoopTools.

8 Installation and running the code

The paper documents installation, model compilation, modular sample programs, and representative MSSM output for relic-density, detection, annihilation, Higgs-decay, and neutrino-telescope observables.

  • Installation and compilation: micrOMEGAs is downloaded as micromegas_3.X.tgz and compiled with gmake or make, with compiler settings adjustable in CalcHEP_src/FlagsForSh.A model executable is then built from its directory with [g]make main=main.c or another supported C, FORTRAN, or C++ source.
  • Installation and compilation: A new model project is created with ./newProject modelName, after which CalcHEP files go in work/models/ and auxiliary codes in lib/.Each model includes sample C and Fortran programs composed of independently selectable modules.
  • Runtime modules: Available modules cover masses, constraints, HiggsBounds, relic density, indirect detection, nucleon and nucleus scattering, neutrino signals, and selected loop-induced annihilation channels.The SHOWPLOTS preprocessor command generates CalcHEP plots when enabled.
  • Sample MSSM output: The sample MSSM run reports Xf=2.65e+01 and Omega=1.03e-01, with an annihilation cross section of 9.22E-27 cm^3/s.The output also lists annihilation-channel contributions and photon, positron, and antiproton fluxes.
  • Sample MSSM output: The same sample reports proton and neutron SI and SD cross sections, solar neutrino and muon fluxes, Higgs branching fractions, and sparticle decay information.The run uses the Suspect spectrum calculator and checks physical constraints including MassLimits.

A Analytical solution of neutrino flux

For non-self-conjugate dark matter, the number-density equations admit an analytical solution under equilibrium and negligible-evaporation assumptions. After equilibrium, the annihilation rate is determined by capture rates and α under an assumed equality of annihilation coefficients.

  • Analytical solution: An analytical number-density solution applies when non-self-conjugate dark matter reaches equilibrium and evaporation is negligible.These are explicit assumptions for solving the number-density equations analytically.
  • Analytical solution: After equilibrium, the annihilation rate depends on the capture rates and α.The passage frames the post-equilibrium rate in terms of capture rather than an independently specified annihilation history.
  • Analytical solution: The derivation assumes equal annihilation coefficients, A¯χ¯χ = Aχχ.This equality is an additional condition in the post-equilibrium treatment.

B Global Parameters

micrOMEGAs exposes global parameters with documented default values, including nucleon quark form factors, and allows their numerical values to be reset anywhere in the code.

  • Global parameters and their default values are listed in Tables 2 and 3.
  • The numerical value of any listed global parameter can be reset anywhere in the code.
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