RelExt: A New Dark Matter Tool for the Exploration of Dark Matter Models

TL;DR

RelExt provides a LO relic-density calculator and efficient parameter-scanning framework for SM extensions with a $Z_2$-stabilized DM candidate. The tool automatically generates $2\to 2$ (co-)annihilation amplitudes from FeynRules, computes thermally averaged cross sections with $s$-channel widths, and solves the Boltzmann equation to yield $\Omega h^2$, while enabling comprehensive scans to locate regions compatible with experiment. It supports pre-implemented models (CxSM, N2HDM-DDP, CPVDM, TRSM, BDM5) and can incorporate new models via a single FeynRules input; it also interfaces with ScannerS and BSMPT for broader theoretical and cosmological constraints. Validation against MicrOMEGAs shows generally good agreement, with differences primarily arising from the treatment of mediator widths near resonances, underscoring the importance of width modeling in accurate relic-density predictions. Overall, RelExt offers a compact, extensible platform to constrain DM models by demanding relic-density saturation within observational bounds and to guide further model-building and phenomenology.

Abstract

We present the C++ program RelExt for Standard Model (SM) extensions that feature a Dark Matter (DM) candidate. The tool allows to efficiently scan the parameter spaces of these models to find parameter combinations that lead to relic density values which are compatible with the measured value within the uncertainty specified by the user. The code computes the relic density for freeze-out (co-)annihilation processes. The user can choose between several pre-installed models or any arbitrary other model featuring a discrete $\mathbb{Z}_2$ symmetry, by solely providing the corresponding FeynRules model files. The code automatically generates the required (co-)annihilation amplitudes and thermally averaged cross sections, including the total widths in the $s$-channel mediators, and solves the Boltzmann equation to determine the relic density. It can easily be linked to other tools like e.g.~ScannerS to check for the relevant theoretical and experimental constraints, or to BSMPT to investigate the phase history of the model and possibly related gravitational waves signals.

Figures (10)

• Figure 1: Flowchart of the code.
• Figure 2: Relic density for the real singlet model, as a function of the DM mass computed with RelExt or MicrOMEGAs. For the orange and red points, we used MicrOMEGAs and set the Higgs portal coupling to 0.1 and 6, respectively. For the green and black points, we used RelExt and also set the Higgs portal coupling to 0.1 and 6, respectively.
• Figure 3: Absolute value for the relative difference of the relic densities calculated with RelExt and MicrOMEGAs, respectively, as a function of the DM mass, for the model CP in the Dark.
• Figure 4: Absolute value for the relative difference of the relic densities calculated with RelExt and MicrOMEGAs, respectively, as a function of $m_{h_{\text{non-SM}}}/m_{DM}$ (left) and $\Gamma_{h_{\text{non-SM}}}$ (right), for the dark doublet phase of the N2HDM. Here, $m_{h_{\text{non-SM}}}$ is the mass of the additional non-SM-like Higgs boson in the visible sector, and $\Gamma_{h_{{\text{non-SM}}}}$ its width.
• Figure 5: Dark Matter annihilation cross section $\sigma(\text{DM DM} \to W^+W^-)$ in pb, as a function of the center-of-mass energy $\sqrt{s}$ in GeV, for the dark doublet phase of the N2HDM. The black points are obtained with RelExt and the red points with MicrOMEGAs.