Shape function in QED and bound muon decays

TL;DR

This paper derives an analytical shape function for particle decay spectra in external fields, accounting for particle motion and interactions, with applications to muonium decay and muons in atoms.

Contribution

It introduces a new analytical shape function that models decay spectra considering external fields and bound states, advancing understanding of such decay processes.

Findings

Derived an explicit analytical expression for the shape function.

Applied the shape function to muonium decay spectrum analysis.

Discussed implications for muons bound in atomic systems.

Abstract

When a particle decays in an external field, the energy spectrum of the products is smeared. We derive an analytical expression for the shape function accounting for the motion of the decaying particle and the final state interactions. We apply our result to calculate the muonium decay spectrum and comment on applications to the muon bound in an atom.