Gearing up for the next generation of LFV experiments, via on-shell methods

TL;DR

This paper uses on-shell amplitude methods within the Standard Model Effective Field Theory to analyze how upcoming experimental bounds on Lepton Flavor Violating processes can be interpreted, emphasizing two-loop operator mixing effects.

Contribution

It introduces on-shell amplitude techniques to classify and compute two-loop operator mixing in the SM EFT relevant for LFV observables, enhancing theoretical precision.

Findings

On-shell methods simplify calculation of anomalous dimensions.

Two-loop operator mixing significantly impacts LFV bounds.

EFT approach clarifies new physics interpretations in models with vector-like fermions.

Abstract

Lepton Flavor Violating (LFV) observables such as $\mu\to e\gamma$, $\mu\to 3e$ and $\mu N \to eN$ are among the best probes for new physics at the TeV scale. In the near future the bounds on these observables will improve by many orders of magnitude. In this work we use the SM EFT to understand the impact of these measurements. The precision reach is such that the interpretation of the bounds requires an analysis of the dimension-six operator mixing up to the two-loop level. Using on-shell amplitude techniques, which make transparent many selection rules, we classify and calculate the different operator mixing chains. At the leading order, on-shell techniques allow to calculate anomalous dimensions of SM EFT operators from the product of tree-level amplitudes, even for two-loop renormalization group mixings. We illustrate the importance of our EFT approach in models with extra vector-like fermions.