# Effective approach to lepton observables: the seesaw case

## TL;DR

This paper derives the low-energy effective field theory for the seesaw extension of the Standard Model with sterile neutrinos, enabling precise predictions of lepton observables and establishing correlations among them, even for very high new physics scales.

## Contribution

It systematically computes one-loop Wilson coefficients for the seesaw model, linking high-scale parameters to low-energy observables and providing a framework to compare different models via spurion analysis.

## Key findings

- Flavor-conserving Wilson coefficients bound flavor-violating ones.
- Low-energy limits strongly suppress flavor violation in various processes.
- Precision measurements impose stringent bounds on new physics scales.

## Abstract

In the absence of direct evidence of new physics, any ultraviolet theory can be reduced to its specific set of low-energy effective operators. As a case study, we derive the effective field theory for the seesaw extension of the Standard Model, with sterile neutrinos of mass $M>m_W$. We systematically compute all Wilson coefficients generated at one loop. Hence, it becomes straightforward to (i) identify the seesaw parameters compatible with the smallness of neutrino masses; (ii) compute precision lepton observables, which may be sensitive to scales as large as $M\sim 10^3$ TeV; and (iii) establish sharp correlations among those observables. We find that the flavour-conserving Wilson coefficients set an upper bound on the flavour-violating ones. The low-energy limits on $\mu\to e$ and $\tau\to e,\mu$ transitions suppress flavour violation in $Z$ and Higgs decays, as well as electric dipole moments, far beyond the experimental reach. The precision measurements of $G_F$, $m_W$, and $Z$ partial decay widths set more stringent bounds than present and future limits on $\tau\to e,\mu$ transitions. We also present a general spurion analysis, to compare the seesaw with different models, thus assessing the discriminating potential of the effective approach.