Low-scale leptogenesis with low-energy Dirac CP -violation

We study the freeze-in scenario of leptogenesis via oscillations within the type-I seesaw model with two quasidegenerate heavy Majorana neutrinos ${N}_{1,2}$ having masses ${M}_{2}>{M}_{1}\ensuremath{\sim}(0.1--100)\text{ }\text{ }\mathrm{GeV}$, $({M}_{2}\ensuremath{-}{M}_{1})/{M}_{1}\ensuremath{\ll}1$, focusing on the role of the $CP$-violation provided by the Dirac phase $\ensuremath{\delta}$ of the Pontecorvo-Maki-Nakagawa-Sakata lepton mixing matrix. We find that viable leptogenesis can be due solely to $CP$-violating values of $\ensuremath{\delta}$ and that the ${N}_{1,2}$ total mixing squared ${\mathrm{\ensuremath{\Theta}}}^{2}={\ensuremath{\sum}}_{\ensuremath{\alpha}}{\mathrm{\ensuremath{\Theta}}}_{\ensuremath{\alpha}}^{2}$ needed is within the reach of future experiments, ${\mathrm{\ensuremath{\Theta}}}_{\ensuremath{\alpha}}$ parametrizing the coupling to the charged lepton $\ensuremath{\alpha}=e$, $\ensuremath{\mu}$, $\ensuremath{\tau}$. Furthermore, the required parameter space differs from that associated with additional Casas-Ibarra sources of $CP$-violation. Future determination of $\ensuremath{\delta}$, ${\mathrm{\ensuremath{\Theta}}}^{2}$ and/or the ratios ${\mathrm{\ensuremath{\Theta}}}_{\ensuremath{\tau}}^{2}\ensuremath{\mathbin:}{\mathrm{\ensuremath{\Theta}}}_{\ensuremath{\mu}}^{2}\ensuremath{\mathbin:}{\mathrm{\ensuremath{\Theta}}}_{e}^{2}$ would provide a critical test of the considered scenario.