Forbidden dark matter annihilation into leptons with full collision terms

The standard approach of calculating the relic density of thermally produced dark matter based on the assumption of kinetic equilibrium is known to fail for forbidden dark matter models since only the high momentum tail of the dark matter phase space distribution function contributes significantly to dark matter annihilations. Furthermore, it is known that the computationally less expensive Fokker-Planck approximation for the collision term describing elastic scattering processes between non-relativistic dark matter particles and the Standard Model thermal bath breaks down if both scattering partners are close in mass. This, however, is the defining feature of the forbidden dark matter paradigm. In this paper, we therefore include the full elastic collision term in the full momentum-dependent Boltzmann equation as well as in a set of fluid equations that couple the evolution of the number density and dark matter temperature for a simplified model featuring forbidden dark matter annihilations into muon or tau leptons through a scalar mediator. On the technical side, we perform all angular integrals in the full collision term analytically and take into account the effect of dark matter self-interactions on the relic density. The overall phenomenological outcome is that the updated relic density calculation results in a significant reduction of the experimentally allowed parameter space compared to the traditional approach, which solves only for the abundance. In addition, almost the entire currently viable parameter space can be probed with CMB-S4, next-generation beam-dump experiments or at a future high-luminosity electron-position collider, except for the resonant region where the mediator corresponds to approximately twice the muon or tau mass.Comment: 23 pages, 6 figure

The dipole formalism for massive initial-state particles and its application to dark matter calculations

The dark matter abundance plays a crucial role in the determination of the valid parameter space of models both in case of a discovery of dark matter and in the context of exclusion limits. Reliable theoretical predictions of the dark matter relic density require technically demanding precision calculations, which were so far limited in their automation due to challenges in the treatment of infrared divergences appearing in higher order calculations. In particular, massive initial states need to be considered in early Universe computations, so that the known dipole subtraction methods could not be directly exploited. We therefore provide a full generalization of the dipole subtraction method by Catani and Seymour to (SUSY)-QCD with massive initial states. All dipole splitting functions and their integrated counterparts are given explicitly for four different dimensional schemes. To showcase their application, we apply our results to dark matter (co)-annihilation processes in the context of the Minimal Supersymmetric (SUSY) Standard Model (MSSM). We also demonstrate the accuracy of the dipole method by comparing our numerical results with those obtained with the space space slicing method. Our analytical results will facilitate future automation of dark matter abundance calculations at next-to-leading order for both SUSY and non-SUSY models.Comment: 42 pages, 8 figures, 3 table

Precision predictions for dark matter with DM@NLO in the MSSM

International audienceWe present DM@NLO, a Fortran 77 based program with a C++ interface dedicated to precision calculations of dark matter (DM) (co)annihilation cross-sections and elastic dark matter-nucleon scattering amplitudes in the Minimal Supersymmetric (SUSY) Standard Model (MSSM) at next-to-leading order (NLO) in perturbative (SUSY) QCD. If the annihilating initial particles carry an electric or colour charge, the Sommerfeld enhanced cross section is included as well and can be matched to the NLO cross section. We review these calculations including technical details relevant for using the code. We illustrate their impact by applying DM@NLO to an example scenario in the constrained MSSM