Selecting mu -> e Conversion Targets to distinguish Lepton Flavour-Changing Operators

TL;DR

Future $$ conversion experiments will significantly improve sensitivity, enabling the potential to constrain multiple operator coefficients and distinguish underlying new physics scenarios, though some operator types remain challenging to differentiate.

Contribution

This work introduces a vector space framework to analyze nuclear target sensitivities, identifying which operator combinations can be constrained and highlighting the need for dedicated nuclear calculations for certain operators.

Findings

Most SI operator combinations can be constrained by future experiments.

Discriminating SD operators requires dedicated nuclear calculations.

A large number of operator directions remain unconstrained, indicating flat directions in parameter space.

Abstract

The experimental sensitivity to $\mu \to e$ conversion on nuclei is set to improve by four orders of magnitude in coming years. However, various operator coefficients add coherently in the amplitude for $\mu \to e$ conversion, weighted by nucleus-dependent functions, and therefore in the event of a detection, identifying the relevant new physics scenarios could be difficult. Using a representation of the nuclear targets as vectors in coefficient space, whose components are the weighting functions, we quantify the expectation that different nuclear targets could give different constraints.We show that all but two combinations of the 10 Spin-Independent (SI) coefficients could be constrained by future measurements, but discriminating among the axial, tensor and pseudoscalar operators that contribute to the Spin-Dependent (SD) process would require dedicated nuclear calculations. We anticipate that $\mu \to e$ conversion could constrain 10 to 14 combinations of coefficients; if $\mu \to e \gamma$ and $\mu \to 3e$ constrain eight more, that leaves 60 to 64 "flat directions" in the basis of QED$\times$QCD-invariant operators which describe $\mu \to e$ flavour change below $m_W$.