Abstract
The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV has previously been evaluated up to NLO in Standard Model couplings (g ∼ 2/3) in relativistic (M ∼ πT) and non-relativistic regimes (M ≫ πT), and up to LO in an ultrarelativistic regime (M ≲ gT). The last result necessitates an all-orders resummation of the loop expansion, accounting for multiple soft scatterings of the nearly light-like particles participating in 1 ↔ 2 reactions. In this paper we suggest howthe regimes can be interpolated into a result applicable for any right-handed neutrino mass and at all temperatures above 160GeV. The results can also be used for determining the lepton number washout rate in models containing right-handed neutrinos. Numerical results are given in a tabulated form permitting for their incorporation into leptogenesis codes. We note that due to effects from soft Higgs bosons there is a narrow intermediate regime around (M ∼ g1/2T in which our interpolation is phenomenological and a more precise study would be welcome.
Highlights
The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV has previously been evaluated up to next-to-leading order (NLO) in Standard Model couplings (g ∼ 2/3) in relativistic (M ∼ πT ) and non-relativistic regimes (M ≫ πT ), and up to LO in an ultrarelativistic regime (M gT )
One observable we consider is the production rate of right-handed neutrinos from an initial state in which the Standard Model particles are in equilibrium at a temperature T, whereas the right-handed neutrinos appear with an abundance much smaller than the equilibrium one
It is difficult to identify a precise reason for the discrepancy, but let us note that if the considerations of section 6 were omitted, i.e. the doubly Bose-enhanced contributions from massless Higgs bosons were included in the NLO expression, our numerical results would be larger by a factor ∼ 1.7 at M ≪ T
Summary
The retarded correlator ΠR can be expressed as an analytic continuation of a corresponding imaginary-time one, 1/T In these equations, Zν is a renormalization factor related to the neutrino Yukawa couplings; K ≡ (kn, k) where kn denotes a fermionic Matsubara frequency; X ≡ (τ, x) is a Euclidean space-time coordinate; φ = iσ2φ∗ is a Higgs doublet; aL, aR are chiral projectors; l is a lefthanded lepton doublet; and . Where the space-time dimension has been expressed as D = 4 − 2ǫ; ht is the renormalized top Yukawa coupling; Nc ≡ 3 is the number of colours; and g1, g2 are the renormalized hypercharge and weak gauge couplings, respectively. At a finite temperature this is no longer the case (cf. figure 4(right)), even Im ΠR turns out to display only a modest dependence on k for fixed M , and allows us to present results in a relatively economic fashion (i.e. as a sparse table)
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