Spontaneous Leptogenesis in Type I Seesaw

TL;DR

This work addresses spontaneous leptogenesis in Type-I seesaw models with spontaneously broken $U(1)_{B-L}$, where the Majoron’s kinetic background provides a CP-violating source. It develops a Boltzmann framework that incorporates both right-handed neutrino decays and $B-L$-violating equilibration driven by inverse decays in the presence of a Majoron background, with a helicity-dependent chemical potential. The key findings show that when the Yukawa coupling is large enough ($K \gtrsim 4$), the final $B-L$ asymmetry approaches its equilibrium value, while for intermediate couplings ($K \sim 1$) decay and inverse-decay compete and the outcome depends on initial RHN abundance, with possible cancellations around $K \simeq 0.3$. The results provide a robust, generalizable framework for spontaneous leptogenesis applicable to a broad class of Majoron-augmented neutrino mass models.

Abstract

Type-I seesaw models with a spontaneously broken $B-L$ symmetry provide a natural framework for spontaneous leptogenesis driven by a Majoron. The kinetic background of the Majoron acts as a CP-violating source, generating a lepton asymmetry both through the decay of right-handed neutrinos and through equilibration via inverse-decay processes. We construct the Boltzmann equations in a fully consistent manner, incorporating both effects, to enable a quantitative analysis. When the neutrino Yukawa coupling is large enough to maintain $B-L$ violating interactions in thermal equilibrium, the resulting asymmetry closely tracks its equilibrium value. In contrast, when this condition is not satisfied, a nontrivial interplay emerges between decay and inverse-decay dynamics, determined by the Yukawa coupling strength and the initial abundance of right-handed neutrinos.

Figures (3)

• Figure 1: Evolution of $\gamma_{D,M, ID}$ in terms of $z=m_N/T$.
• Figure 2: Evolution of the normalized $Y_{B-L}$ for various values of $K$. The dashed green (red) lines show the contribution from the decay (inverse-decay) processes alone, while the solid orange curves represent their combined effect. The solid blue curves display the ratio $Y_N/Y_N^{eq}$, and the dotted curves indicate the inverse-decay rate normalized to the Hubble rate. The upper and lower panels correspond to the initial conditions $Y_N(0)=0$ and $Y_N(0)=Y_N^{\rm eq}$, respectively.
• Figure 3: Final yield of the $B-L$ asymmetry in units of $y_{\theta1} \varepsilon_1$ as a function of $K$ for two different initial conditions of $Y_N(0)=0$ and $Y_N^{\rm eq}$.