Precision study of GeV-scale resonant leptogenesis

Abstract

Low-scale leptogenesis is most efficient in the limit of an extreme mass degeneracy of right-handed neutrino flavours. Two variants of this situation are of particular interest: large neutrino Yukawa couplings, which boost the prospects of experimental scrutiny, and small ones, which may lead to large lepton asymmetries surviving down to T < 5 GeV. We study benchmarks of these cases within a "complete" framework which tracks both helicity states of right-handed neutrinos as well as their kinetic non-equilibrium, and includes a number of effects not accounted for previously. For two right-handed flavours with GeV-scale masses, Yukawa couplings up to |h| ∼ 0.7 × 10 −5 are found to be viable for baryogenesis, with ∆M/M ∼ 10 −8 as the optimal degeneracy. Late-time lepton asymmetries are most favourably produced with ∆M/M ∼ 10 −11 . We show that the system reaches a stationary state at T < 15 GeV, in which lepton asymmetries can be more than 10 3 times larger than the baryon asymmetry, reach flavour equilibrium, and balance against helicity asymmetries.Keywords: Thermal Field Theory, CP violation, Neutrino Physics, Resummation crossover is at T ∼ 160 GeV [30,31], and therefore we may find ourselves on the side of the Higgs phase 1 in this situation.Our study is based on a quantum field theoretic formalism that we have developed in a series of previous papers [15,20,26], drawing upon earlier investigations [32][33][34][35][36]. The system is characterized by a number of slow equilibration rates, which are mediated by neutrino Yukawa couplings and are of magnitude ∼ |h| 2 g 2 T /π, where g 2 ≡ 4πα is a generic Standard Model coupling, as well as by a slow flavour oscillation rate, which is of magnitude ∼ |M 2 2 − M 2 1 |/k. The slow rates imply that right-handed neutrinos are neither in chemical, nor in kinetic, nor in helicity, nor in flavour equilibrium, and need to be tracked through density matrices. The equilibration rates contain both "direct" and "indirect" contributions, with the former referring to 1 ↔ 2 and 2 ↔ 2 decays or scatterings and the latter to rates experienced by off-shell left-handed neutrinos, which subsequently "oscillate" into right-handed neutrinos thanks to the presence of the Higgs mechanism at T < ∼ 160 GeV.The plan of this paper is as follows. After reviewing the overall theoretical framework in sec. 2 and the parametrization of a charge-asymmetric ensemble in the presence of a Higgs mechanism in sec. 3, we discuss the structure of the indirect contribution in sec. 4, keeping consistently track of both helicity states. All ingredients appearing in the rate coefficients are computed in sec. 5, generalizing previous results in order to account for both helicity states and the presence of chemical potentials. The direct contributions are discussed in sec. 6, again resolving existing results to the chemical potential assignments relevant for the Higgs phase. The resulting system is solved numerically in an approximate form in sec. 7, in order to identify relevant corners of the parameter space. ...

Kinetic equations for sterile neutrinos from thermal fluctuations

“…Deep in the Higgs phase (T ≪ 130 GeV) the susceptibilities have a non-trivial dependence on the temperature. They have been studied in [37]. 26…”

“…25 See equations (4.5) and (4.6) of reference [19]. 26 See appendix A of reference [37]. sterile neutrino, plus the same process with additional soft scatterings, which are sometimes referred to as 1n ↔ 2n processes, also contribute at leading order [38].…”

A thermal neutrino interaction rate at NLO

“…The influence on lepton asymmetries is a bit larger, however by considering the benchmark point from ref. [37], chosen because lepton asymmetry production continues for a long time in this case, we found a reduction of lepton asymmetries by ∼ 1%. Hence it appears that for practical applications it is sufficient to use the simple leading-order expression for Γ u from eq.…”

“…For this, the parameters have been fixed as in ref. [37]. A partial cancellation between contributions from various domains of p ⊥ can be observed, as a result of which the final magnitude of the negative NLO correction remains at a modest ∼ 15% level at high temperatures.…”

“…Even if the whole integral is UV finite, it was argued in ref. [37] that it is reasonable to adopt a phenomenological cutoff |p ⊥ | ≤ 2k ∼ 2πT . Adopting this prescription, which amounts to a partial inclusion of higher order contributions in an expansion in ∼ m 2 i /k 2 , transverse integrals evaluate to…”