𝜃23 = π/4 and δ = −π/2 in neutrino mixing, which convention?

Abstract

Considerable information has been obtained about neutrino mixing matrix. Present data show that in the particle data group (PDG) parametrization, the 2–3 mixing angle and the CP violating phase are consistent with [Formula: see text] and [Formula: see text], respectively. A lot of efforts have been devoted to constructing models in realizing a mixing matrix with these values. However, the particular angles and phase are parametrization convention dependent. The meaning about the specific values for mixing angle and phase needs to be clarified. Using the well-known nine independent ways of parametrizing the mixing matrix, we show in detail how the mixing angles and phase change with conventions even with the 2–3 mixing angle to be [Formula: see text] and the CP violating phase to be [Formula: see text]. The original Kobayashi–Maskawa and an additional one belong to such a category. The other 6 parametrizations have mixing angles and phase very different values from those in the PDG parametrization although the physical effects are the same. Therefore one should give the specific parametrization convention when making statements about values for mixing angles and phase.