$CP$ Violation in Neutrino Oscillation and Leptogenesis

We study the correlation between $CP$ violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable $CP$ phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant $J$ as well as neutrinoless double $\beta$ decay by identifying a low energy $CP$-violating phase which signals the $CP$-violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and $J$ is obtained. We also study the effect coming from the phases which are not related to leptogenesis.

Figure 1

The maximum possible lepton number density ($-Y_L$) as a function of $x_1$ for three different $M_1$. From top to bottom, $M_1=(3,2,\mathrm{\text{and}}1)\times {10}^{11}\mathrm{G}\mathrm{e}\mathrm{V}$.

Figure 2

Lepton number density ($-Y_L$) as a function of $x_2$ for $M_1=2\times {10}^{11}\mathrm{G}\mathrm{e}\mathrm{V}$. Solid line corresponds to $x_1=0.01\mathrm{e}\mathrm{V}$. The long dashed line corresponds to $x_1=0.03\mathrm{e}\mathrm{V}$, and the dotted line corresponds to $x_1=0.05\mathrm{e}\mathrm{V}$.

Figure 3

Correlation between lepton number asymmetry ${\epsilon }_1$ and neutrino $CP$ violation $J$, for $M_1=2\times {10}^{11}\mathrm{G}\mathrm{e}\mathrm{V}$. The large (small) contour corresponds to $x_1=0.03(0.01)\mathrm{e}\mathrm{V}$. The thick solid lines show the allowed region from baryogenesis.