Completeness and Complementarity for $\mu \to e \gamma$, $\mu \to 3e$ and $\mu \to e$ conversion

TL;DR

This paper introduces a method using observable-vectors in operator coefficient space to analyze the complementarity of muon-to-electron LFV processes, aiding in understanding new physics despite many unconstrained operators.

Contribution

It proposes a novel framework of observable-vectors to identify the combined operator coefficients probed by different LFV processes, enhancing the analysis of their complementarity.

Findings

Observable-vectors overlap with most operator coefficients.

LFV processes provide complementary information about new physics.

Updated sensitivities of LFV processes to operator coefficients.

Abstract

Lepton Flavour Violation(LFV) is New Physics that must occur, but is stringently constrained by experiments searching for mu to e flavour change, such as $\mu \to e \gamma$, $\mu \to 3e$ and $\mu \to e$ conversion. However, in an Effective Field Theory(EFT) parametrisation, there are many more $\mu \leftrightarrow e$ operators than restrictive constraints, so determining operator coefficients from data is a remote dream. It is nonetheless interesting to learn about New Physics from data, so this manuscript introduces "observable-vectors" in the space of operator coefficients, which identify at any scale the combination of coefficients probed by the observable. These vectors have at least partpermil overlap with most of the coefficients, and are used to study whether $\mu \to e \gamma$, $\mu \to 3e$ and $\mu \to e$ conversion give complementary information about New Physics. The appendix gives updated sensitivities of these processes, (and a subset of LFV tau decays), to operator coefficients at the weak scale in the SMEFT and in the EFT below mW.