Resonant $s$-channel dark matter annihilation at NLO

Understand

Studies of dark matter annihilation through an $s$-channel resonance are often based on recipes such as a narrow width approximation or real intermediate state subtraction.

• We review a recipe-free formalism that can be implemented at the NLO level in the full theory, and ensures the cancellation of mass singularities.
• Its basic ingredients can be formulated in the relativistic regime, but we show that the procedure simplifies if we go to the non-relativistic one and assume the presence of kinetic equilibrium.
• The latter case is illustrated for scalar singlet dark matter with $m_{\rm S}^{ } \simeq 60$ GeV, freezing out at $T \simeq (1-3)$ GeV, re-confirming the viability of this scenario with couplings tiny enough to evade experimental constraints.