RT Journal Article
T1 Relativistic ⟨ σ v rel ⟩ in the calculation of relics abundances : a closer look
A1 Cannoni, Mirco
AB In this paper we clarify the relation between the invariant relativistic relative velocity Vr, the Møller velocity ¯v, and the nonrelativistic relative velocity vr. Adopting Vr as the true physical relative velocity for pair collisions in a nondegenerate relativistic gas, we show that in the frame comoving with the gas (i) a probability density function P(Vr) for Vr exists, (ii) an exact formula for the mean value ⟨Vr⟩ exists, (iii) the thermally averaged cross section times relative velocity ⟨σvrel⟩ that appears in the density evolution equation for thermal relics is reformulated only in terms of Vr and P(Vr) in a manifestly Lorentz invariant form, and (iv) the frame-dependent issues of the standard formulation in terms of the Møller velocity, as well as “superluminal” relative velocities, are not present in this formulation. Furthermore, considering the annihilation of dark matter into a particle-antiparticle pair f¯f, in the cases mf=0, mf=m, and mf≫m, we find that the coefficients of the low velocity expansion of ⟨σVr⟩ admit an exact analytical representation in terms of the Meijer G functions that can be reduced to combinations of modified Bessel functions of the second kind.
PB American Physical Society
SN 2470-0010
SN 2470-0029 (electrónico)
YR 2014
FD 2014
LK http://hdl.handle.net/10272/13585
UL http://hdl.handle.net/10272/13585
LA eng
NO Cannoni, M.: "Relativistic ⟨ σ v rel ⟩ in the calculation of relics abundances : a closer look". Physical Review D. Vol. 89, n. 10, (2014). DOI: 10.1103/PhysRevD.89.103533
NO The author acknowledges N. Fornengo and M. Peiro for useful discussions during the 9th MultiDark workshop, Halcala de Henares, November 6-9, 2013, Spain, where some of the results of the present paper were presented. Work supported in part by MultiDark under Grant No. CSD2009-00064 of the Spanish MICINN Consolider-Ingenio 2010 Program. Further support is provided by the MICINN Project FPA2011-23781 and by the Grant MICINN-INFN(PG21) AIC-D-2011-0724.
DS Repositorio Institucional de la Universidad de Huelva
RD 1 jun 2026