Abstract
We consider effective operators describing Dark Matter (DM) interactions with Standard Model fermions. In the non-relativistic limit of the DM field, the operators can be organized according to their mass dimension and their velocity behaviour, i.e. whether they describe s- or p-wave annihilations. The analysis is carried out for self-conjugate DM (real scalar or Majorana fermion). In this case, the helicity suppression at work in the annihilation into fermions is lifted by electroweak bremsstrahlung. We construct and study all dimension-8 operators encoding such an effect. These results are of interest in indirect DM searches.
Highlights
Significant experimental activity is currently devoted to the search for Dark Matter (DM) by looking at the excesses in cosmic ray production through DM annihilations in the galactic halo.Detailed predictions for the fluxes largely depend on the particle physics model for the DM, e.g.the mass, the annihilation channels etc
If we want to describe the annihilation of two non-relativistic DM particles, whose relative velocity is v ∼ 10−3 in our Galaxy today, it is convenient to expand the cross section in powers of v vσ = a + b v2 + O(v4), (1.1)
We have considered the annihilation of a self-conjugate DM particle – either a Majorana fermion or a real scalar – into light SM fermions
Summary
Significant experimental activity is currently devoted to the search for Dark Matter (DM) by looking at the excesses in cosmic ray production through DM annihilations (or decays) in the galactic halo. The EFT is only applicable whenever there is a separation of scales between the process to describe (the annihilation of non-relativistic DM at a scale ∼ MDM) and the underlying microscopic physics of the interactions (at a scale Λ). This may not always be the case, as, for example, in the case of supersymmetry with a compressed spectrum. In this paper we will classify the operators (up to dimension 8) according to the v-behaviour of the amplitude connecting two self-conjugate particles – real scalars or Majorana fermions – in the initial state with the final state of two massless fermions and possibly a gauge boson. We collect some useful relations and identities in the Appendices, for the convenience of the reader
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