A lower bound on the right-handed neutrino mass from leptogenesis

TL;DR

This paper proves a model-independent upper bound on the CP asymmetry $|\epsilon_1|$ in the decay of the lightest right-handed neutrino within the hierarchical seesaw framework, showing $|\epsilon_1| \lesssim \frac{3}{8 \pi} \frac{M_1}{\langle H_u^0\rangle^2} (m_3 - m_1)$. Using the Casas–Ibarra parametrization, it demonstrates that $\epsilon_1$ is not independent of $M_1$ once the light-neutrino mass scale is fixed. Consequently, achieving the observed baryon asymmetry with thermal production requires $M_1 \gtrsim 10^9$ GeV and a reheat temperature $T_{reh} \gtrsim 10^{10}$ GeV, placing tension with gravitino bounds. Non-thermal production scenarios can evade some of these constraints, but still impose lower bounds related to the decay temperature $T_\Gamma$, highlighting the interplay between high-scale neutrino physics and early-Universe cosmology. The work clarifies the link between CP violation, neutrino masses, and cosmological constraints in leptogenesis.

Abstract

In the seesaw model, the baryon asymmetry of the Universe can be generated by the decay of the lightest right-handed neutrino, nu_R. For a hierarchical spectrum of right-handed neutrinos, we show that there is a model independent upper bound on the CP asymmetry produced in these decays: epsilon < 3 m_{nu_3} M_{nu_R}/(8 pi <H_u>^2). This implies that epsilon and the mass M_{nu_R} of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If m_{nu_3} = sqrt{Delta m^2_{atm}} and the nu_R are produced thermally, then leptogenesis requires a reheat temperature of the Universe T_{reh} > M_{nu_R} > 10^8 GeV. Reasonable estimates of nu_R production and the subsequent washout of the asymmetry, as made by Buchmuller and Plumacher, imply M_{nu_R} > 10^9 GeV, and T_{reh} > 10^{10} GeV. Implications for the gravitino problem are also discussed.