GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations

Abstract

Abstract:Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1 + n ↔ 2 + n scatterings and for all 2 ↔ 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.

Kinetic equations for sterile neutrinos from thermal fluctuations

“…In [19] the chemical potential for L α appears in f F instead of the one for X α , which is nevertheless consistent, see section 4. Unlike the equation in [19], our (3.38) contains not only scattering contributions, but also dispersive ones, see section 5.1. In [19] the latter are incorporated at a later stage.…”

“…There the kinetic equations are given in terms of the retarded correlator of J as a function of slowly varying chemical potentials, like in our (3.38). The terms multiplying these correlators are given to linear 12 See equation (2.29) of reference [19]. 13 The helicity diagonal contribution containing the v-spinors in [19] is not consistent with our equation (3.38).…”

“…Aside from that, the first term in the curly bracket in (3.38) (which contains the u-spinors) is equivalent to the corresponding one in [19]. 13 For vanishing Majorana masses (3.39) coincides with the corresponding equation in [19]. 14 Furthermore, for non-vanishing Majorana masses, our contributions containing the u-spinors also appear there.…”

“…In [19] the latter are incorporated at a later stage. Aside from that, the first term in the curly bracket in (3.38) (which contains the u-spinors) is equivalent to the corresponding one in [19]. 13 For vanishing Majorana masses (3.39) coincides with the corresponding equation in [19].…”

“…When electroweak sphalerons are in equilibrium, our statistical operator which determines ∆ α contains µ Xα X α , but no separate chemical potential for baryon number because the latter is not conserved. In reference [19] µ α L α + µ B B appears. However, using the equilibrium conditions one can match the coefficients which gives µ α = µ Xα , and µ B = − α µ Xα /3.…”