Deviations from tribimaximal neutrino mixing in the type-II seesaw model and leptogenesis

Current experimental data allow the zero value for one neutrino mass, either $m_1=0$ or $m_3=0$. This observation implies that a realistic neutrino mass texture can be established by starting from the limit (a) $m_1=m_2=0$ and $m_3\ne 0$ or (b) $m_1=m_2\ne 0$ and $m_3=0$. In both cases, we may introduce a particular perturbation which ensures the resultant neutrino mixing matrix to be the tribimaximal mixing pattern or its viable variations with all entries being formed from small integers and their square roots. We find that it is natural to incorporate this kind of neutrino mass matrix in the minimal type-II seesaw model with only one heavy right-handed Majorana neutrino $N$ in addition to the $\mathrm{SU}(2{)}_L$ Higgs triplet ${\Delta }_L$. We show that it is possible to account for the cosmological baryon number asymmetry in the $m_3=0$ case via thermal leptogenesis, in which the one-loop vertex correction to $N$ decays is mediated by ${\Delta }_L$ and the $CP$-violating asymmetry of $N$ decays is attributed to the electron flavor.

Figure 1

Parameter space of $|x|$ and $\epsilon$ constrained by current experimental data on $m_1$, $m_2$, ${\theta }_{12}$, and ${\eta }_B$ in the minimal type-II seesaw model with $m_3=0$.

Figure 2

Parameter space of $M$ and $\arg (x)$ constrained by current experimental data on $m_1$, $m_2$, ${\theta }_{12}$, and ${\eta }_B$ in the minimal type-II seesaw model with $m_3=0$.