Radiative Corrections to the Sum Rule of Lepton Flavor Mixing
摘要: The simple correlation among three lepton flavor mixing angles (θ12,θ13,θ23) and the leptonic Dirac CP-violating phase δ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the sum rule θ12≈θν12+θ13cosδ, where θν12 stems from a constant mixing pattern in the neutrino sector and takes the value of θν12=45∘ for the bi-maximal mixing (BM), θν12=35.3∘ for the tri-bimaximal mixing (TBM) or θν12=tan−1[2/(5√+1)]≈31.7∘ for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. Quantitatively, we implement the Bayesian approach to explore the posterior distribution of δ at the low-energy scale, which becomes quite broad when the RG running effects are significant, as in the minimal supersymmetric standard model (MSSM) with a sizeable value of tanβ. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.