Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay

We make an attempt to study the impact of renormalization-group equations (RGE) induced $\mu -\tau$ reflection symmetry breaking on the effective Majorana neutrino mass $\mathrm{\mid }⟨m{⟩}_{ee}\mathrm{\mid }$ in neutrinoless double beta ($0\nu \beta \beta$) decay. At present, the $0\nu \beta \beta$ decay serves as a unique process to address the Majorana nature of massive neutrinos. The rate of such decay process depends on $\mathrm{\mid }⟨m{⟩}_{ee}\mathrm{\mid }$. On the other hand, $\mu -\tau$ reflection symmetry predicts ${\theta }_{23}={45}^{\circ }$ and $ \delta = \pm 90^\circ $togetherwithtrivialvaluesoftheMajoranaCP-phases($ \rho, \sigma $). Moreover, based on the recent global best-fit values which prefer higher octant of ${\theta }_{23}$ and third quadrant of $\delta$, it is hard to believe the exactness of such symmetry. Also, any non-trivial values of $\rho ,\sigma$ may have some significant impact on $\mathrm{\mid }⟨m{⟩}_{ee}\mathrm{\mid }$. In this context, we study the spontaneous breaking of the symmetry via one-loop RGE-running from a superhigh energy scale (${\mathrm{\Lambda }}_{\mu \tau }$) down to the electroweak scale (${\mathrm{\Lambda }}_{\mathrm{E}\mathrm{W}}$). Given the broken symmetry, we perform some systematic analysis for $\mathrm{\mid }⟨m{⟩}_{ee}\mathrm{\mid }$ in substantial detail. Further, we also extend this analysis for other lepton-number violating effective Majorana masses.