Comprehensive Analysis of Charged Lepton Flavour Violation in the Symmetry Protected Type-I Seesaw

TL;DR

This paper provides a comprehensive calculation of one-loop corrections to charged lepton flavour violation in the symmetry protected type-I seesaw model, including matching to effective field theory and numerical analysis of observable correlations.

Contribution

It offers the first complete one-loop correction calculations and effective field theory matching for charged lepton flavour violation in the symmetry protected type-I seesaw model.

Findings

Calculates one-loop corrections both exactly and at leading order in the seesaw expansion.

Performs matching onto the Standard Model Effective Field Theory at dimension-6.

Analyzes correlations among various charged lepton flavour violating processes.

Abstract

The type-I seesaw model is probably the most straightforward and best studied extension of the Standard Model that can account for the tiny active neutrino masses determined from neutrino oscillation data. In this article, we calculate the complete set of one-loop corrections to charged lepton flavour violating processes within this model. We give the results both using exact diagonalisation of the neutrino mass matrix, and at at leading order in the seesaw expansion (i.e. $\mathcal{O}(v^2/M_R^2)$). Furthermore, we perform the matching onto the $SU(2)_L$ invariant Standard Model Effective Field Theory at the dimension-6 level. These results can be used as initial conditions for the renormalisation group evolution from the right-handed neutrino scale down to the scale of the physical processes, which resums large logarithms. In our numerical analysis, we study the inverse seesaw limit, i.e. the symmetry protected type-I seesaw, where the Wilson coefficient of the Weinberg operator is zero such that sizeable neutrino Yukawas are permissible and relevant effects in charged lepton flavour violating observables are possible. We correlate the different charged lepton flavour violating processes, e.g. $\ell\to\ell^\prime\gamma$, $\ell\to3\ell^\prime$, $\mu\to e$ conversion and $Z\to \ell\ell^\prime$, taking into account the constraints from electroweak precision observables and tests of lepton flavour universality.