Renormalization Group Evolution of the Non-Unitary operator

TL;DR

This paper investigates how non-unitarity in the lepton mixing matrix, arising from dimension six operators in the Type-I seesaw mechanism, evolves with energy scale via renormalization group equations.

Contribution

It provides a detailed analysis of the renormalization group evolution of non-unitary operators in the context of the Type-I seesaw mechanism.

Findings

Non-unitarity originates at high energy scales.

Renormalization group running affects the magnitude of non-unitarity.

Implications for neutrino oscillation experiments.

Abstract

Integrating out a heavy field gives rise to effective Lagrangian containing higher dimensional operators. In the context of Type-I seesaw mechanism, integrating out the heavy right handed neutrino field leads to unique dimension five operator which gives the tree level neutrino mass term. Apart from these there are dimension six operators that can have important implications. A linear combination of two such operators gives rise to the non-unitarity in the lepton mixing matrix, $U_{\text{PMNS}}$. In this paper, we discuss the origin of non-unitarity at the high scale and its evolution through renormalization group running.