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

The pattern of neutrino mixing, usually parameterized by the Pontecorvo-Maki-Nakagawa- Sakata 𝑈PMNS matrix, still remains a striking puzzle in particle physics. 𝑈PMNS 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 𝑈SO3 and the CP-conserving phases 𝛿CP=0◦ and 180◦. The mixing matrix 𝑈SO3 with cyclic order of the Lie group generators implies 𝛿CP=180◦ for clockwise rotation in three dimensions, a viable scenario for normal mass ordering. We determine a range of rotation angles for 𝑈SO3 which deviate substantially from the almost maximal mixings in the standard 𝑈PMNS scenario, yielding ‘democratic’ values for the mixing angles. On the other hand, 𝛿CP=0◦ CP-conserving case supports near-maximal mixing scenario. With the fixed 𝛿CP value, the 𝑈SO3 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 𝑈SO3 neutrino mixing parameterization is suited for independent CP-conserving neutrino oscillation experimental analysis.