Abstract:
The finite temperature higher order corrections to the annihilation cross section of Majorana and Dirac type dark matter candidates are presented considering a model in which the dark matter, χ, annihilates to Standard Model fermion pairs via a scalar portal having Yukawa interaction, L ⊃ (λ χPL f − ϕ+ + h.c.). The finite temperature corrections are computed for virtual photon corrections to the cross section for the process χχ → f f at next-to-leading order in the QED coupling constant as well as to real photon emission and absorption process χχ → f f (γ). Techniques of thermal field theory are used in order to calculate these finite temperature corrections. At finite temperature there are no ultraviolet divergences due to the presence of the Bose-Einstein or Fermi-Dirac distribution functions which act as a regulator; however, infra-red and collinear divergences are still present. The generalized technique of Grammer and Yennie is used to factorise the photon propagator into an infra-red-safe and infra-red-divergent part in order to deal with the soft divergences. The cancellation of infra-red divergences among complementary diagrams between the virtual photon correction and real photon correction to the dark matter annihilation process at next-to-leading order (at O(α)) is shown. It is noted that the thermal correction in the virtual case appears due to the finite temperature terms in the photon and fermion propagators whereas the thermal correction in the real photon case appears due to finite temperature terms in the phase space factors. In this study, the mediator scalar is considered to be heavy compared to the dark matter particles and fermions mϕ > mχ ≫ m f. The cross section at both leading and next-to-leading order is found to be helicity suppressed for Majorana dark matter, whereas helicity suppression is lifted for Dirac dark matter. Finally, the dominant thermal corrections to the dark matter annihilation cross section at this order are presented, keeping terms up to quadratic order in fermion mass m²f at O(T²).
