Renormalization Group Running of the Neutrino Mass Operator in Extra Dimensions

Abstract

We study the renormalization group (RG) running of the neutrino masses and the leptonic mixing parameters in two different extra-dimensional models, namely, the Universal Extra Dimensions (UED) model and a model, where the Standard Model (SM) bosons probe an extra dimension and the SM fermions are confined to a four-dimensional brane. In particular, we derive the beta function for the neutrino mass operator in the UED model. We also rederive the beta function for the charged-lepton Yukawa coupling, and confirm some of the existing results in the literature. The generic features of the RG running of the neutrino parameters within the two models are analyzed and, in particular, we observe a power-law behavior for the running. We note that the running of the leptonic mixing angle θ_{12} can be sizable, while the running of θ_{23} and θ_{13} is always negligible. In addition, we show that the tri-bimaximal and the bimaximal mixing patterns at a high-energy scale are compatible with low-energy experimental data, while a tri-small mixing pattern is not. Finally, we perform a numerical scan over the low-energy parameter space to infer the high-energy distribution of the parameters. Using this scan, we also demonstrate how the high-energy θ_{12} is correlated with the smallest neutrino mass and the Majorana phases.