Consequences of a CP-Transformed $\mu \tau$-Flavored Friedberg-Lee Symmetry in a Neutrino Mass Model

Abstract

We propose a neutrino mass model with a generalized $\mu \tau$-flavored CP symmetry assuming the light Majorana neutrino mass term enjoys an invariance under a generalized Friedberg-Lee (FL) transformation. While both Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is dictated as a consequence of FL symmetry. For both NO and IO, we show that the atmospheric mixing angle $\theta _{23}\ne \pi /4$. The Dirac CP phase $\delta =\pi /2,3\pi /2$ for IO and nearly maximal for NO due to $\cos \delta \propto \sin \theta _{13}$. For the NO, very tiny CP violation might arise through one of the Majorana phases, namely, $\beta$. Beside fitting the neutrino oscillation data, we present a study of $\nu _\mu \rightarrow \nu _e$ oscillation which is expected to reveal Dirac CP violation in long-baseline experiments. We also calculate the Ultra High Energy (UHE) neutrino flavor flux ratios at neutrino telescopes, from which statements regarding the octant of $\theta _{23}$ have been made in our model.