RT Journal Article
T1 Relativistic and nonrelativistic annihilation of dark matter: a sanity check using an effective field theory approach
A1 Cannoni, Mirco
AB We find an exact formula for the thermally averagedcross section times the relative velocity  σvrel  with relativisticMaxwell–Boltzmann statistics. The formula is validin the effective field theory approach when the masses ofthe annihilation products can be neglected compared withthe dark matter mass and cut-off scale. The expansion atx = m/T ≫ 1 directly gives the nonrelativistic limit of σvrel , which is usually used to compute the relic abundancefor heavy particles that decouple when they are nonrelativistic.We compare this expansion with the one obtained byexpanding the total cross section σ(s) in powers of the nonrelativisticrelative velocity vr . We show the correct invariantprocedure that gives the nonrelativistic average  σnrvr  nrcoinciding with the large x expansion of  σvrel  in the comovingframe. We explicitly formulate flux, cross section, thermalaverage, collision integral of the Boltzmann equation inan invariant way using the true relativistic relative vrel, showingthe uselessness of the Møller velocity and further elucidatingthe conceptual and numerical inconsistencies relatedwith its use.
PB SpringerOpen
SN 1434-6044
YR 2016
FD 2016-03
LK http://hdl.handle.net/10272/18542
UL http://hdl.handle.net/10272/18542
LA eng
NO Cannoni, M. (2016). Relativistic and nonrelativistic annihilation of dark matter: a sanity check using an effective field theory approach. The European Physical Journal C, 76(3). DOI: https://doi.org/10.1140/epjc/s10052-016-3991-2
DS Repositorio Institucional de la Universidad de Huelva
RD 1 jun 2026