An effective field theory for muon conversion and muon decay-in-orbit

TL;DR

This paper develops a comprehensive effective field theory framework combining multiple EFTs to accurately predict muon conversion and decay-in-orbit rates and signal shapes, crucial for upcoming experimental searches for charged lepton flavor violation.

Contribution

It introduces a systematic multi-EFT approach to improve predictions of muon conversion and decay-in-orbit processes below the nuclear scale, addressing complex multi-scale effects.

Findings

Derived a factorization theorem for muon processes.

Provided the most accurate signal shape predictions.

Established renormalization group equations for the framework.

Abstract

Muon conversion is one of the best probes of charged lepton flavor violation. The experimental limit is soon expected to improve by four orders of magnitude, thus calling for precise predictions of the shape of the signal spectrum. Equally important are precise predictions for muon decay-in-orbit, the main background for muon conversion. While the calculation of electromagnetic corrections to the two processes above the nuclear scale does not involve significant challenges, it becomes substantially more complex below that scale due to multiple scales, bound-state effects and experimental setup. Here, we present a systematic framework that addresses these challenges by resorting to a series of effective field theories. Combining Heavy Quark Effective Theory (HQET), Non-Relativistic QED (NRQED), potential NRQED, Soft-Collinear Effective Theory I and II, and boosted HQET, we derive a factorization theorem and present the renormalization group equations. Our framework allows for the proper calculation of precise predictions for the rates of the two processes, with crucial implications for the upcoming muon conversion searches. We also provide the most accurate prediction of the signal shape for those searches.