$\theta_{23}=\pi/4$ and $\delta=-\pi/2$ 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) parameterization, the 2-3 mixing angle and the CP violating phase are consistent with $\theta_{23} = \pi/4$ and $\delta_{PDG} = -\pi/2$, 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 parameterization convention dependent. The meaning about the specific values for mixing angle and phase needs to be clarified. Using the well known 9 independent ways of parameterizing 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 $\pi/4$ and the CP violating phase to be $-\pi/2$. The original Kaobayashi-Maskawa and an additional one belong to such a category. The other 6 parameterizations have mixing angles and phase very different values from those in the PDG parameterization although the physical effects are the same. Therefore one should give the specific parameterization convention when making statements about values for mixing angles and phase.