Quark lepton complementarity and renormalization group effects

Abstract

We consider a scenario for the Quark-Lepton Complementarity relations between mixing angles in which the bi-maximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle θ_{12} is \sim 1σ(1.5 - 2^\circ) above the best fit point coinciding practically with the tri-bimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to θ_{12} as well as to θ_{13} in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in large part of the parameter space corrections Δθ_{12} are small or negligible. In the MSSM version of the scenario the correction Δθ_{12} is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of ν_1 and ν_2 when leading contributions to θ_{12} running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of ν_1 and ν_2: ϕ> π/2.