Source-linked AI summary
micrOMEGAs4.1: two dark matter candidates
G. Belanger, F. Boudjema, A. Pukhov, A. Semenov
TL;DR
The paper addresses dark matter scenarios requiring more than one candidate by extending micrOMEGAs to handle two dark sectors. It generalizes relic-density calculations to include conversion and semi-annihilation, adds corresponding direct- and indirect-detection analyses, and demonstrates the framework in a scalar doublet–singlet model.
Problem
Signals at different mass scales and dark matter models with multiple WIMPs motivate methods that can treat more than one dark matter candidate and their interactions.
Method
micrOMEGAs is extended with coupled Boltzmann equations for two dark sectors, including dark matter conversion and semi-annihilation, plus direct- and indirect-detection routines.
Results
The framework computes the contributions of each component to the dark matter density and is illustrated with a Z4-symmetric scalar doublet–singlet model containing two stable candidates.
Takeaways & Limitations
Two-component dark matter observables can be evaluated within micrOMEGAs, including relic density, conversion, semi-annihilation, and detection signals.
Takeaways & Limitations
The model-independent mdlIndep routines and the legacy darkOmega function do not support models with two dark matter particles or sectors.
Abstract
from arXiv · showhide
micrOMEGAs is a code to compute dark matter observables in generic extensions of the standard model. This version of micrOMEGAs includes a generalization of the Boltzmann equations to take into account the possibility of two dark matter candidates. The modification of the relic density calculation to include interactions between the two DM sectors as well as semi-annihilation is presented. Both DM signals in direct and indirect detection are computed as well. An extension of the standard model with two scalar doublets and a singlet is used as an example.
1 Introduction
The paper extends micrOMEGAs to dark matter models with two sectors, motivated by multiple signals and enabled by discrete symmetries supporting two stable candidates. It classifies allowed interactions and illustrates the framework with a Z4 model containing two scalar doublets and a singlet.
- 1 Introduction: Multiple direct- and indirect-detection anomalies and signals across different mass scales motivate considering more than one dark matter candidate.The simplest WIMP paradigm is challenged by collider data, while some anomalies suggest cross sections above the canonical cosmological value.
- 1 Introduction: micrOMEGAs generalizes relic-density calculations to include dark-matter conversion, semi-annihilation, and contributions from each component.The updated routines also account for signals in direct and indirect detection.
- 1 Introduction: A working example extends the Standard Model with two scalar doublets and a singlet under Z4, yielding two dark matter candidates and semi-annihilation.H2 and S are inert, while H1 has couplings similar to those of the Standard Model Higgs.
- 1 Introduction: Discrete symmetries can produce multiple dark sectors whose lightest particles are stable or conditionally stable dark matter candidates.The paper discusses Z2 × Z′2 and Z4 examples, with sector assignments determined by discrete charges.
- 1 Introduction: The paper classifies dimension-4 interactions for two dark sectors and identifies discrete groups that generate the corresponding scalar interaction structures.For fermions and gauge bosons, the allowed interaction terms are more limited and are adapted to each symmetry and particle content.
3 Relic density computation
The relic-density calculation evolves two coupled dark-sector abundances while incorporating annihilation, coannihilation, conversion, and semi-annihilation. Because the resulting equations can be stiff, micrOMEGAs uses specialized numerical treatment and cross-section tabulation.
- 3.1 Evolution equations: The derivation assumes thermal equilibrium within each sector, a common kinetic temperature with the Standard Model, and departure from equilibrium when interaction rates become too low.Only the processes allowed by a particular model are included in the thermally averaged cross sections.
- 3.1 Evolution equations: The two-sector number-density equations include annihilation, coannihilation, dark-matter conversion, and semi-annihilation processes.Conversion has the form φαφβ → φγφδ, while semi-annihilation has the form φαφβ → φγX with X a Standard Model particle.
- 3.1 Evolution equations: The equations are formulated for abundances Ya = na/s and converted from time evolution using entropy conservation.The calculation introduces deviations from equilibrium, ∆Ya = Ya − Ȳa.
- 3.2 Solution of equations: Two-component evolution can become stiff when the dark matter masses differ substantially, because the heavy and light components freeze out at different temperatures.The resulting attractor-line behavior causes standard direct integration to stall.
- 3.2 Solution of equations: micrOMEGAs solves the stiff equations with a backward Rosenbrock algorithm and tabulates cross sections over temperature to speed the calculation.The tabulation interval is T ∈ [Tend, Tstart], with Tend = 10^-3 GeV.
4 Two DM models in micrOMEGAs
micrOMEGAs4.X adds routines for two-component relic-density and signal calculations, while retaining one-component functionality with explicit scope limitations.
- Initialization: The particle-naming convention distinguishes the second dark sector with names beginning with two tildes, and sortOddParticles initializes the relevant global parameters.
- Relic density: darkOmega2 calculates Ωh2 for one- and two-component dark-matter models and provides the CDM2 mass fraction through fracCDM2.The recommended fast option has approximately 1% accuracy, with Beps controlling included coannihilation channels.
- Detection observables: The fracCDM2 parameter feeds total direct, indirect, and neutrino-telescope signals, and users may modify it for Milky Way fractions.
- Scope limitations: The previous darkOmega routine is appropriate only for one dark-matter sector because it does not distinguish discrete-symmetry classes.
- Detection observables: Nucleon amplitudes and cross sections are computed separately for each dark-matter candidate without rescaling for its density fraction.
- Scope limitations: Model-independent routines in mdlIndep do not account for two dark-matter particles and depend only on the global Mcdm parameter.
5 Example
The benchmark Z4 model contains singlet and doublet dark sectors with two candidates, and its micrOMEGAs output reports their masses, relic abundances, annihilation processes, and nucleon amplitudes.
- Relic density: The example compares abundances including DM conversion and semi-annihilation with cases in which these processes are ignored.
- Model and benchmark: The Z4 benchmark has singlet candidate ~sc at 578 GeV and doublet candidate ~~X at 895.5 GeV.The doublet sector also contains ~~H+ and ~~H3, while either H0 or A0 can be the doublet dark matter candidate.
- Relic density: The benchmark relic abundances are omega1=5.91E-02 and omega2=6.14E-02.
- Relic density: The reported annihilation cross section is 5.89E-26 cm^3/s, with contributions led by mixed-sector processes into Z and h final states.
- Direct detection: For ~sc, the reported nucleon spin-independent cross sections are 1.813E-09 pb for protons and 1.831E-09 pb for neutrons.
- Direct detection: For ~~X, the reported nucleon spin-independent cross sections are 3.473E-10 pb for protons and 3.543E-10 pb for neutrons.
Appendix
The appendix introduces a two-singlet Z5 model whose potential is valid for arbitrary ZN symmetries and includes dark-sector interactions absent from the example Z4 model.
- Z5 model: The Z5 model adds singlets S1 and S2 to the Standard Model Higgs doublet and assigns them charges 1/5 and −3/5.
- Potential: Its potential contains a symmetry-independent part valid for any ZN choice and is specified by scalar masses and couplings.
- Dark-sector interactions: Each dark sector contains one particle, with interactions between sectors such as S1S1 → S†1S†2 that are absent from the considered Z4 model.
- Implementation: The Z5 model and LanHEP source are provided in the Z5M directory for generating CalcHEP model files.