Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations

TL;DR

This paper identifies a minimal flavor symmetry in the seesaw mechanism that explains neutrino oscillation data, predicts relations between mixing matrices, and constrains neutrino flavor textures.

Contribution

It reveals a novel minimal flavor symmetry underlying the seesaw mechanism that links light and heavy neutrino mixing matrices and explains observed CP violation.

Findings

Equalities |U_{μi}| = |U_{τi}| and |R_{μi}| = |R_{τi}| derived from data

Invariance of neutrino mass term under a generalized μ-τ reflection symmetry

Constraints on flavor textures of active and sterile neutrinos

Abstract

In the canonical seesaw framework flavor mixing and CP violation in weak charged-current interactions of light and heavy Majorana neutrinos are correlated with each other and described respectively by the $3\times 3$ matrices $U$ and $R$. We show that the very possibility of $\big|U^{}_{\mu i}\big| = \big|U^{}_{\tau i}\big|$ (for $i = 1, 2, 3$), which is strongly indicated by current neutrino oscillation data, automatically leads to a novel prediction $\big|R^{}_{\mu i}\big| = \big|R^{}_{\tau i}\big|$ (for $i = 1, 2, 3$). We prove that behind these two sets of equalities and the experimental evidence for leptonic CP violation lies a minimal flavor symmetry -- the overall neutrino mass term keeps invariant when the left-handed neutrino fields transform as $\nu^{}_{e \rm L} \to (\nu^{}_{e \rm L})^c$, $\nu^{}_{\mu \rm L} \to (\nu^{}_{\tau \rm L})^c$, $\nu^{}_{\tau \rm L} \to (\nu^{}_{\mu \rm L})^c$ and the right-handed neutrino fields undergo an arbitrary unitary CP transformation. Such a generalized $\mu$-$\tau$ reflection symmetry may help constrain the flavor textures of active and sterile neutrinos to some extent in the seesaw mechanism.