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

The pattern of neutrino mixing, usually parameterized by the Pontecorvo–Maki–Nakagawa– Sakata U PMNS matrix, still remains a striking puzzle in particle physics. U 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 SO3 and the CP-conserving phases δ C P = 0 ∘ and 180 ∘ . The mixing matrix U SO3 with cyclic order of the Lie group generators implies δ CP = 180 ∘ for clockwise rotation in three dimensions, a viable scenario for normal mass ordering. We determine a range of rotation angles for U SO3 which deviate substantially from the almost maximal mixings in the standard U PMNS scenario, yielding ‘democratic’ values for the mixing angles. On the other hand, δ C P = 0 ∘ CP-conserving case supports near-maximal mixing scenario. With the fixed δ CP value, the U 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 SO3 neutrino mixing parameterization is suited for independent CP-conserving neutrino oscillation experimental analysis.