Renormalization group evolution of neutrino masses and mixing in the Type-III seesaw mechanism

TL;DR

This paper analyzes how neutrino masses and mixing parameters evolve with energy in the Type-III seesaw model, emphasizing the impact of threshold effects and Majorana phases on the renormalization group evolution.

Contribution

It provides a detailed calculation of the renormalization group equations for neutrino parameters in the Type-III seesaw model, including threshold effects and a basis that remains well-defined at all angles.

Findings

Threshold effects significantly influence neutrino mixing evolution.

Majorana phases impact the running of mixing angles.

A basis is used where all parameters are well-defined at $ heta_{13} = 0$.

Abstract

We consider the standard model extended by heavy right handed fermions transforming as triplets under SU(2)$_L$, which generate neutrino masses through the Type-III seesaw mechanism. At energies below their respective mass scales, the heavy fields get sequentially decoupled to give an effective dimension-5 operator. Above their mass thresholds, these fields also participate in the renormalization of the wavefunctions, masses and coupling constants. We compute the renormalization group evolution of the effective neutrino mass matrix in this model, with particular emphasis on the threshold effects. The evolution equations are obtained in a basis of neutrino parameters where all the quantities are well-defined everywhere, including at $\theta_{13} = 0$. We also point out the important role of the threshold effects and Majorana phases in the evolution of mixing angles through illustrative examples.