Investigating two-zero texture in the light of gauged Type-II seesaw

Neutrino oscillation, discovered over two decades ago, confirmed that neutrinos have nonzero masses. Since then, two mass-squared differences have been measured with unprecedented precision, yet the absolute neutrino mass scale remains unknown. Additionally, the fundamental symmetry governing the neutrino mixing pattern is still undetermined. Among various theoretical possibilities, the two-zero texture in the neutrino mass matrix ($m_\nu$) stands out as an attractive framework due to its reduced number of free parameters, enabling definite predictions for the unknown parameters of the PMNS matrix. In this work, we present a comprehensive analysis of the two-zero texture, focusing on its implications for the Dirac CP phase ($\delta$), the Majorana phases ($\rho$, $\sigma$) and the effective Majorana mass ($m_{\beta\beta}$), the latter being crucial for neutrinoless double beta decay. We find that for certain two-zero textures, $m_{\beta\beta}$ reaches a few tens of meV, placing it within the sensitivity range of KamLAND-Zen. Furthermore, we demonstrate how a two-zero texture can naturally emerge in a well-motivated neutrino mass model, specifically the gauged Type-II seesaw mechanism, which requires multiple scalar triplets. Notably, some of the two-zero patterns cannot be realized in this framework, as more than two independent zeros appear in $m_\nu$. Finally, we discuss key phenomenological consequences of the gauged Type-II seesaw model.