Dirac mass matrix textures and the lightest right-handed neutrino mass scale in Type I seesaw leptogenesis

TL;DR

This work investigates the type I seesaw mechanism and vanilla leptogenesis in the two-flavor regime to backward-engineer Dirac-mass textures that fix the lightest right-handed neutrino mass. By imposing two-flavor leptogenesis conditions, the authors derive six general Dirac-mass textures $M_D^{\rm I}$–$M_D^{\rm VI}$ that yield $Y_L^{(1)}=0$, $Y_L^{(3)}=0$ with equal washout masses $\tilde{m}_{1\alpha}$ and specific CP-violation structures, which in turn constrain the lightest RH-neutrino mass to $M_1$ in $10^{9}\, ext{GeV} \lesssim M_1 \lesssim 10^{12}\, ext{GeV}$. They illustrate two concrete textures: one reproducing a known two-flavor scenario and a new texture $M_D^{\rm IV}$ with a distinct CP-structure yielding $\epsilon_{1e},\epsilon_{1\mu},\epsilon_{1\tau}$ relations, while both preserving the same $M_1$ window. The results provide concrete texture-motivated guidance for model building in the Type I seesaw, linking Dirac-mass structures to the viable range of the lightest RH-neutrino mass and suggesting avenues for extending the analysis to unflavored and three-flavor regimes. Overall, the paper identifies six textures that guarantee two-flavor leptogenesis and offers explicit examples, contributing to the understanding of how neutrino-mass generation frameworks constrain high-scale physics.

Abstract

The type I seesaw mechanism is one of the leading proposed explanations for how neutrinos acquire their tiny masses. However, the mass scale of the undiscovered right-handed neutrinos required by this mechanism remains undetermined. Assuming vanilla leptogenesis in the two-flavor regime, we work backwards to find the required general textures of the Dirac mass matrix from which we determine the mass of the lightest right-handed neutrino to be around $10^9 {\rm GeV}$ to $10^{12} {\rm GeV}$.