QED corrections to bound-muon decays from an effective-field-theory framework

Abstract

Bound-muon decays are a powerful probe of new physics, making precise theoretical predictions for their spectra essential. While QED corrections significantly affect the shape of the spectra, their calculation is extremely challenging below the nuclear scale. By exploring the universality of modern effective-field-theory techniques, we present a framework that systematically computes those corrections across a broad class of bound-muon decays. As a key application, we provide the most accurate predictions to date for the signal and background spectra in muon conversion. We show that radiative corrections modify the leading-order ratio of these spectra by $5\%$ with minimal energy dependence, a result relevant for enhancing the discovery reach of upcoming experiments. Our framework also represents a crucial step toward connecting high-energy physics to low-energy observables, complementing recent progress above the muon mass scale.

Figures (2)

• Figure 1: Normalized cumulant distributions for muon DIO, conversion and their ratio in the endpoint region of the electron spectrum. While the DIO and conversion curves show sizable, energy-dependent corrections exceeding $10\%$, their ratio remains $5\%$ and exhibits only a very weak energy dependence. See text for details.
• Figure 2: Feynman diagrams for the 2-loop photon-mediated interactions between muon and nucleus in muon conversion (first row) and DIO (second and third rows). The black disks represent the high-energy CLFV effective interaction, the white ones the Fermi interaction, and the gray ones the interaction between a photon and a non-point-like nucleus.