Connecting low energy leptonic $CP$ violation to leptogenesis

It was commonly thought that the observation of low energy leptonic $CP$-violating phases would not automatically imply the existence of a baryon asymmetry in the leptogenesis scenario. This conclusion does not generically hold when the issue of flavor is relevant and properly taken into account in leptogenesis. We illustrate this point with various examples studying the correlation between the baryon asymmetry and the $CP$-violating asymmetry in neutrino oscillations and the effective Majorana mass in neutrinoless double beta decay.

Figure 1

The invariant $J_{CP}$ versus the baryon asymmetry varying (in blue) $\delta =[0,2\pi ]$ in the case of hierarchical RH neutrinos and NH light neutrino mass spectrum for $s_{13}=0.2$, ${\alpha }_{32}=0$, $R_{12}=0.86$, $R_{13}=0.5$ and $M_1=5\times {10}^{11}\mathrm{GeV}$. The red region denotes the $2\sigma$ range for the baryon asymmetry.

Figure 2

The baryon asymmetry $|Y_{\mathrm{B}}|$ versus the effective Majorana mass in neutrinoless double beta decay, $⟨m_{\nu }⟩$, in the case of Majorana $CP$-violation, hierarchical RH neutrinos and IH light neutrino mass spectrum, for $\delta =0$, $s_{13}=0$, purely imaginary $R_{11}{R}_{12}$, $|R_{11}|=1.05$ and $M_1=2\times {10}^{11}\mathrm{GeV}$. The Majorana phase ${\alpha }_{21}$ is varied in the interval $[-\pi /2,\pi /2]$.

Figure 3

The quantity $|⟨m_{\nu }⟩|$ versus the baryon asymmetry varying ${\alpha }_{32}$ between 0 and $\pi /3$ for the case of degenerate RH neutrinos and QD for light neutrinos for $\delta =\pi /3$, $s_{13}=0.01$, $M_1={10}^{10}\mathrm{GeV}$ and $m=0.1\mathrm{eV}$.