SpontaneousCPviolation in lepton-sector: A common origin forθ13, the DiracCPphase, and leptogenesis

Abstract

A possible interplay between the two terms of the general type-II seesaw formula is exercised which leads to the generation of nonzero ${\ensuremath{\theta}}_{13}$. The specific flavor structure of the model, guided by the ${A}_{4}\ifmmode\times\else\texttimes\fi{}{Z}_{4}\ifmmode\times\else\texttimes\fi{}{Z}_{3}$ symmetry and accompanied with the Standard Model singlet flavons, yields the conventional seesaw contribution to produce the tribimaximal lepton mixing which is further corrected by the presence of the $SU(2{)}_{L}$ triplet contribution to accommodate ${\ensuremath{\theta}}_{13}$. We consider the $CP$ symmetry to be spontaneously broken by the complex vacuum expectation value (vev) of a singlet field $S$. While the magnitude of its complex vev is responsible for generating ${\ensuremath{\theta}}_{13}$, its phase part induces the low energy $CP$ violating phase ($\ensuremath{\delta}$) and the $CP$ violation required for leptogenesis. Hence the triplet contribution, although subdominant, plays a crucial role in providing a common source for nonzero ${\ensuremath{\theta}}_{13}$, $\ensuremath{\delta}$ and $CP$-violation required for leptogenesis. We find that the recent hint for $\ensuremath{\delta}$ close to $3\ensuremath{\pi}/2$ is somewhat favored in this setup though it excludes the exact equality with $3\ensuremath{\pi}/2$. We also discuss the generation of lepton asymmetry in this scenario.