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

Abstract

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 $|⟨m{⟩}_{ee}|$ 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 $|⟨m{⟩}_{ee}|$. On the other hand, $\mu -\tau$ reflection symmetry predicts ${\theta }_{23}=45^{\circ }$ and $\delta =\pm 90^{\circ }$ together with trivial values of the Majorana CP-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 $|⟨m{⟩}_{ee}|$. In this context, we study the spontaneous breaking of the symmetry via one-loop RGE-running from a superhigh energy scale (${\Lambda }_{\mu \tau }$) down to the electroweak scale (${\Lambda }_{\mathrm{EW}}$). Given the broken symmetry, we perform some systematic analysis for $|⟨m{⟩}_{ee}|$ in substantial detail. Further, we also extend this analysis for other lepton-number violating effective Majorana masses.

Comments: v2: 12 pages, 4 figures, 1 table, LaTex format changed. Some more discussion added in section IV-A, conclusion is unchanged. Version accepted for publication in Phys. Rev. D