Towards identifying the minimal flavor symmetry behind neutrino oscillations

Abstract

Current neutrino oscillation data indicate that the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata matrix $U$ exhibits a $μ$-$τ$ flavor interchange symmetry $|U^{}_{μi}| = |U^{}_{τi}|$ (for $i = 1, 2, 3$) as a good approximation. In particular, the T2K measurement implies that the maximal neutrino mixing angle $θ^{}_{23}$ and the CP-violating phase $δ$ should be close to $π/4$ and $-π/2$, respectively. Behind these observations lies a minimal flavor symmetry -- - the effective Majorana neutrino mass term keeps invariant under the transformations $ν^{}_{e \rm L} \to (ν^{}_{e \rm L})^c$, $ν^{}_{μ\rm L} \to (ν^{}_{τ\rm L})^c$ and $ν^{}_{τ\rm L} \to (ν^{}_{μ\rm L})^c$. Extending this flavor symmetry to the canonical seesaw mechanism, we find that the $R$-matrix describing the strength of weak charged-current interactions of heavy Majorana neutrinos satisfies $|R^{}_{μi}| = |R^{}_{τi}|$ as a consequence of $|U^{}_{μi}| = |U^{}_{τi}|$. This result can be used to set a new upper bound, which is about three orders of magnitude more stringent than before, on the flavor mixing factor associated with the charged-lepton-flavor-violating decay mode $τ^- \to e^- + γ$.