Renormalisation Group Corrections to Neutrino Mixing Sum Rules

Abstract

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form ${\tilde{U}}_{\nu }$, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $\delta$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of ${\tilde{U}}_{\nu }$. We consider five extensively discussed possible symmetry forms of ${\tilde{U}}_{\nu }$: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for $\delta$ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.

arXiv comment42 pages, 25 figures; v2 matches version published in JHEP

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