Nuclear-level effective theory of $\mu\rightarrow e$ conversion: Inelastic process

TL;DR

This paper extends the nuclear effective theory of $$ conversion to include inelastic processes in $^{27}$Al, showing that inelastic transitions can provide additional insights into the underlying CLFV operators without new experiments.

Contribution

The authors develop a theoretical framework for inelastic $$ conversion, adding five new response functions and demonstrating their potential to extract more information from existing experimental setups.

Findings

Inelastic $$ responses can distinguish different CLFV operators.

$^{27}$Al is an optimal target for studying inelastic $$ conversion.

Inelastic signals can be observed with anticipated experimental resolution.

Abstract

Mu2e and COMET will search for electrons produced via the neutrinoless conversion of stopped muons bound in 1s atomic orbits of $^{27}$Al, improving existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. Conventionally, $\mu\rightarrow e$ conversion experiments are optimized to detect electrons originating from transitions where the nucleus remains in the ground state, thereby maximizing the energy of the outgoing electron. Clearly, detection of a positive signal in forthcoming experiments would stimulate additional work $-$ including subsequent conversion experiments using complementary nuclear targets $-$ to further constrain the new physics responsible for CLFV. Here we argue that additional information can be extracted without the need for additional experiments, by considering inelastic conversion in $^{27}$Al. Transitions to low-lying nuclear excited states can modify the near-endpoint spectrum of conversion electrons, with the ratio of the elastic and inelastic responses being sensitive to the underlying CLFV operator. We extend the nuclear effective theory of $\mu\rightarrow e$ conversion to the inelastic case, which adds five new response functions to the six that arise for the elastic process. We evaluate these nuclear response functions in $^{27}$Al and calculate the resulting conversion-electron signal, taking into account the resolution anticipated in Mu2e/COMET. We find that $^{27}$Al is an excellent target choice from the perspective of the new information that can be obtained from inelastic $\mu \rightarrow e$ conversion.