On the Maximal CP Violation in Leptogenesis with Two Right Handed Neutrinos

Abstract

We present a generalized exact analytical expression for the upper bound on the CP-violating decay asymmetry in the case of standard vanilla leptogenesis within the minimal type-I seesaw with two Right Handed Neutrinos (RHNs) case scenario as a function of the effective neutrino mass in the hierarchical limit. We derive the bound using a novel analytical treatment of the roots of a quartic equation arising from the conditions for successful leptogenesis, in which the CP asymmetry, effective neutrino mass, and other physical quantities enter as parameters. We find that the upper bound on CP asymmetry is a monotonically increasing function of the effective neutrino mass, asymptotically saturating to a global maximum at the large effective mass regime. We find that our exact analytical expression of the upper bound as a function of the effective neutrino mass is smaller than the previous analytical results in the literature. We also find that the global maximum on CP asymmetry with two RHNs obtained at the large effective mass regime is less than the Davidson-Ibarra bound corresponding to the standard vanilla leptogenesis scenario with three RHNs, leading to a more stringent bound on the lightest RHN mass for the scenario with two RHNs, as expected from some previous results in literature. We find that the deviation from the standard Davidson-Ibarra bound becomes most dramatic for inverted neutrino mass hierarchy, by nearly two orders of magnitude.