Three-zero textures of neutrino mass matrix and leptogenesis in the left-right symmetric model

Within the framework of the left-right symmetric model (LRSM) and under the assumption of a diagonal Dirac neutrino mass matrix $M_{\rm D}$, this paper systematically investigates 20 types of three-zero textures in the Majorana neutrino mass matrix $M_{\rm R}$. The study reveals that only five three-zero textures of $M_{\rm R}$ satisfy the constraints of the latest NuFit 6.0 global fit results. Furthermore, we phenomenologically explore the correlations between Majorana phases $\rho$ and $\sigma$, as well as the relationships between the heavy neutrino mass spectrum $M_{I}~(I=1,2,3)$, ratio of Dirac matrix elements $y_{2}$, $y_{3}$ and the scale factor $r$. The results indicate strong correlations among the model parameters. In particular, the allowed regions for the Majorana CP phases are significantly restricted and depend on the specific texture of $M_{\rm R}$. On this basis, leptogenesis originating from heavy right-handed neutrino decays is investigated. Numerical results demonstrate that the $M_{\nu3}$ pattern can achieve successful leptogenesis within specific $r$ intervals for both the normal ordering (NO) and the inverted ordering (IO) of the light neutrino masses, while the $M_{\nu4}$ and $M_{\nu5}$ patterns possess viable parameter space for successful leptogenesis only in the NO case.