Flavour effects in gravitational leptogenesis

Abstract

Within the Type-I seesaw mechanism, quantum effects of the right-handed (RH) neutrinos in the gravitational background lead to an asymmetric propagation of lepton and anti-leptons which induces a Ricci scalar and neutrino Dirac-Yukawa coupling dependent chemical potential and therefore a lepton asymmetry in equilibrium. At high temperature, lepton number violating scattering processes try to maintain a dynamically generated lepton asymmetry in equilibrium. However, when the temperature drops down, the interactions become weaker, and the asymmetry freezes out. The frozen out asymmetry can act as a pre-existing asymmetry prior to the standard Fukugita-Yanagida leptogenesis phase (Ti ∼ Mi, where Mi is the mass of ith RH neutrino). It is then natural to consider the viability of gravitational leptogenesis for a given RH mass spectrum which is not consistent with successful leptogenesis from decays. Primary threat to this gravity-induced lepton asymmetry to be able to successfully reproduce the observed baryon-to-photon ratio is the lepton number violating washout processes at Ti ∼ Mi. In a minimal seesaw set up with two RH neutrinos, these washout processes are strong enough to erase a pre-existing asymmetry of significant magnitude. We show that when effects of flavour on the washout processes are taken into account, the mechanism opens up the possibility of successful leptogenesis (gravitational) for a mass spectrum M2 » 109GeV » M1 with M1 ≳ 6.3 × 106 GeV. We then briefly discuss how, in general, the mechanism leaves its imprints on the low energy CP phases and absolute light neutrino mass scale.

Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis

“…Here we do not confront the robustness of p = 1 solution (or the 'hierarchically enhanced solution' [43,44]), rather we take it at face value. As an aside, let us mention that p = 0 solution does not work (cannot produce correct baryon asymmetry) in the standard cosmological evolution of the universe [43,44,115]. From now on we shall proceed with hierarchically enhanced equilibrium asymmetry…”

“…Since the lightest RH scale is below 10 9 GeV, a second stage N 1 -washout by inverse decays occurs in all the three flavours and therefore the final asymmetry is given by [115]…”

“…In ref. [115] we computed it numerically and found these effects do not have any significant effect on the final asymmetry. For convenience, let us re-mention here that the frozen out asymmetry that is large enough in magnitude to be compatible with the observed one, corresponds to smaller values κ which are not very sensitive to the flavour effect.…”

“…For convenience, let us re-mention here that the frozen out asymmetry that is large enough in magnitude to be compatible with the observed one, corresponds to smaller values κ which are not very sensitive to the flavour effect. On the other hand, in the probability triangle, though flavour projectors show a biasness towards the electron flavour, P iα = 1/3 still remains a fair choice to take under consideration [115,127]. Therefore to efficiently scan the entire parameter space in the computer codes, we have simplified the final formula for N f B−L considering a democratic behaviour of the flavour projectors.…”

“…A dynamical CPT violation in this process induces a lepton asymmetry in equilibrium which is maintained during the course of evolution until ∆L = 2 N 1 -interaction rates fall below the Hubble expansion rate. While even without flavour effects [108][109][110][111][112][113][114] in the washout processes, the mechanism is able to produce dominant lepton asymmetry (compared to the leptogenesis from decays) [41][42][43][44], when the effects are taken into account, the lightest RH mass scale M 1 can be lowered to M min ∼ 10 7 GeV [115] unlike the standard N 1 -thermal [116][117][118][119] leptogenesis scenario (T RH > M 1 ) where it is subjected to a lower bound of 10 9 GeV [120]. We consider a hierarchical spectrum of RH neutrinos assuming the heaviest mass scale is of the order of the U(1) breaking scale (Λ CS ) which also sets the initial temperature of asymmetry generation and masses of the other two are parametrically suppressed with the lightest being O(M min ).…”