Significance of Broken μ − τ Symmetry in Correlating δ CP , θ 13 , Lightest Neutrino Mass, and Neutrinoless Double Beta Decay 0 ν β β

Abstract

Leptonic CP violating phase ${\delta }_{\text{CP}}$ in the light neutrino sector and leptogenesis via present matter-antimatter asymmetry of the Universe entails each other. Probing CP violation in light neutrino oscillation is one of the challenging tasks today. The reactor mixing angle ${\theta }_{13}$ measured in reactor experiments, LBL, and DUNE with high precision in neutrino experiments indicates towards the vast dimensions of scope to detect ${\delta }_{\text{CP}}$ . The correlation between leptonic Dirac CPV phase ${\delta }_{\text{CP}}$ , reactor mixing angle ${\theta }_{13}$ , lightest neutrino mass $m_1$ , and matter-antimatter asymmetry of the Universe within the framework of $\mu -\tau$ symmetry breaking assuming the type I seesaw dominance is extensively studied here. Here, a SO(10) GUT model with flavor $\mu -\tau$ symmetry is considered. In this work, the idea is to link baryogenesis through leptogenesis and the hint of CP violation in the neutrino oscillation data to a breaking of the mu-tau symmetry. Small tiny breaking of the $\mu -\tau$ symmetry allows a large Dirac CP violating phase in neutrino oscillation which in turn is characterized by awareness of measured value of ${\theta }_{13}$ and to provide a hint towards a better understanding of the experimentally observed near-maximal value of ${\nu }_{\mu }-{\nu }_{\tau }$ mixing angle ${\theta }_{23}\simeq \left(\pi /4\right)$ . Precise breaking of the $\mu -\tau$ symmetry is achieved by adding a 120-plet Higgs to the $10+1\overline{2}6$ -dimensional representation of Higgs. The estimated three-dimensional density parameter space of the lightest neutrino mass $m_1$ , ${\delta }_{\text{CP}}$ , and reactor mixing angle ${\theta }_{13}$ is constrained here for the requirement of producing the observed value of baryon asymmetry of the Universe through the mechanism of leptogenesis. Carrying out numerical analysis, the allowed parameter space of $m_1$ , ${\delta }_{\text{CP}}$ , and ${\theta }_{13}$ is found out which can produce the observed baryon to photon density ratio of the Universe.