CP-conserving SO(3) parameterization of the neutrino mixing matrix

Abstract

The pattern of neutrino mixing, usually parameterized by the Pontecorvo-Maki-Nakagawa-Sakata $U_{\rm PMNS}$ matrix, still remains a striking puzzle in particle physics. $U_{\rm PMNS}$ is one of six possible products of multiplying three Euler matrices. Here we discuss the neutrino mixing matrix parameterization for three known flavours of neutrinos based on the SO(3) group represented by one three-dimensional rotation matrix $U_{\rm SO3}$ and the CP-conserving phases $\delta_{\rm CP}=0^{\circ}$ and $180^\circ$. The mixing matrix $U_{\rm SO3}$ with cyclic order of the Lie group generators implies $\delta_{\rm{CP}}=180^\circ$ for clockwise rotation in three dimensions, a viable scenario for normal mass ordering. We determine a range of rotation angles for $U_{\rm SO3}$ which deviate substantially from the almost maximal mixings in the standard $U_{\rm PMNS}$ scenario, yielding `democratic' values for the mixing angles. On the other hand, $\delta_{\rm CP}=0^{\circ}$ CP-conserving case supports near-maximal mixing scenario. With the fixed $\delta_{\rm CP}$ value, the $U_{\rm SO3}$ parameterization can be validated or falsified by the next generation of neutrinoless double beta decay experiments and puts a stringent constraint on the absolute neutrino mass. The proposed $U_{{\rm SO3}}$ neutrino mixing parameterization is suited for independent CP-conserving neutrino oscillation experimental analysis.