EFT approach to the endpoint of muon decay-in-orbit

TL;DR

This paper extends an Effective Field Theory approach to accurately predict the muon decay-in-orbit spectrum near the endpoint, crucial for future muon conversion experiments, by including complex neutrino-antineutrino final states and achieving high-precision QED corrections.

Contribution

It develops a novel EFT framework to compute the DIO spectrum near the endpoint with next-to-leading logarithmic accuracy, addressing complex neutrino final states.

Findings

Most precise prediction of the DIO spectrum to date

Inclusion of neutrino-antineutrino final states in the EFT framework

Achieved next-to-leading logarithmic prime accuracy for QED corrections

Abstract

As upcoming experiments aim to probe muon conversion with unprecedented precision, equally precise theoretical predictions are crucial to maximize discovery potential. This applies not only to the new physics signal, muon-electron conversion, but also to its only irreducible background, muon decay-in-orbit (DIO) near the endpoint. Accurate computation of higher-order corrections in bound states is a long-standing challenge due to the difficulty of systematically organizing contributions. In previous work, we developed an Effective Field Theory framework to address this issue and applied it to muon conversion. Here, we extend this approach to the DIO endpoint, a more complex problem due to the presence of a neutrino-antineutrino pair in the final state. We present the most precise prediction to date of the background spectrum relevant for future muon conversion searches, achieving next-to-leading logarithmic prime accuracy for QED corrections.