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

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 $\left|U_{\mu i}^{}\right|=\left|U_{\tau i}^{}\right|$ (for $i=1,2,3$), which is strongly indicated by current neutrino oscillation data, automatically leads to a novel prediction $\left|R_{\mu i}^{}\right|=\left|R_{\tau i}^{}\right|$ (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 ${\nu }_{e\mathrm{L}}^{}\to ({\nu }_{e\mathrm{L}}^{}{)}^c$, ${\nu }_{\mu \mathrm{L}}^{}\to ({\nu }_{\tau \mathrm{L}}^{}{)}^c$, ${\nu }_{\tau \mathrm{L}}^{}\to ({\nu }_{\mu \mathrm{L}}^{}{)}^c$ 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.

Comments: LaTeX 16 pages, 2 figures. More discussions and references added. Accepted for publication in JHEP