Correlation between leptonicCPviolation andμ−τsymmetry breaking

Abstract

Considering the {mu}-{tau} symmetry, we discuss a direct linkage between phases of flavor neutrino masses and leptonic CP violation by determining three eigenvectors associated with M=M{sub {nu}}{sup {dagger}}M{sub {nu}} for a complex flavor neutrino mass matrix M{sub {nu}} in the flavor basis. Since the Dirac CP violation is absent in the {mu}-{tau} symmetric limit, leptonic CP violation is sensitive to the {mu}-{tau} symmetry breaking, whose effect can be evaluated by perturbation. It is found that the Dirac phase ({delta}) arises from the {mu}-{tau} symmetry breaking part of M{sub e{mu}}{sub ,e{tau}} and an additional phase ({rho}) is associated with the {mu}-{tau} symmetric part of M{sub e{mu}}{sub ,e{tau}}, where M{sub ij} stands for an ij matrix element (i,j=e,{mu},{tau}). The phase {rho} is redundant and can be removed but leaves its effect in the Dirac CP violation characterized by sin({delta}+{rho}). The perturbative results suggest the exact formula of mixing parameters including that of {delta} and {rho}, which turns out to be free from the effects of the redundant phases. As a result, it is generally shown that the maximal atmospheric neutrino mixing necessarily accompanies either sin{theta}{sub 13}=0 or cos({delta}+{rho})=0, the latter of which indicates maximal CP violation, where {theta}{sub 13} is the {nu}{submore » e}-{nu}{sub {tau}} mixing angle.« less