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Publication# On the effective operators for Dark Matter annihilations

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.

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Fermion

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin 1/2, spin 3/2, etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons).

Majorana fermion

A Majorana fermion (maɪə'rɑːnə), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles. With the exception of neutrinos, all of the Standard Model fermions are known to behave as Dirac fermions at low energy (lower than the electroweak symmetry breaking temperature), and none are Majorana fermions.

Dirac fermion

In physics, a Dirac fermion is a spin-1⁄2 particle (a fermion) which is different from its antiparticle. A vast majority of fermions fall under this category. In particle physics, all fermions in the standard model have distinct antiparticles (perhaps excepting neutrinos) and hence are Dirac fermions. They are named after Paul Dirac, and can be modeled with the Dirac equation. A Dirac fermion is equivalent to two Weyl fermions. The counterpart to a Dirac fermion is a Majorana fermion, a particle that must be its own antiparticle.

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