Reducing \theta_13 to 9 degrees

Abstract

We propose to consider the possibility that the observed value of ${\theta }_{13}$ is not the result of a correction from an initially vanishing value, but rather the result of a correction from an initially larger value. As an explicit example of this approach, we consider analytically and numerically well-known CKM-like charged lepton corrections to a neutrino diagonalization matrix that corresponds to a certain mixing scheme. Usually this results in generating ${\theta }_{13}=9^{\circ }$ from zero. We note here, however, that 9 is not only given by $0+9$, but also by $18-9$. Hence, the extreme case of an initial value of 18 degrees, reduced by charged lepton corrections to 9 degrees, is possible. For some cases under study new sum rules for the mixing parameters, and correlations with CP phases are found.

Comments: 11 pages, 6 figures