Shape function in QED and bound muon decays

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.Comment: 5 pages, 3 figures v2: Corrected verrsion to appear in PR

High-energy electrons from the muon decay in orbit: Radiative corrections

“…In the lower half of the spectrum the muon and the electron can be treated as nearly free and the binding effects can be factorized. Then the radiative corrections, known for a free muon, are convoluted with a shape function that parametrizes the Coulomb field effect [3,7]. Here we construct an expansion around the end-point and employ it to find radiative corrections also to the high-energy part of the spectrum.…”

Mu2e-II: Muon to electron conversion with PIP-II

“…This includes, in particular, the irreducible background of muon decay in orbit (DIO), which features an electron-energy tail up to the signal region E e ∼ m µ due to nuclear recoil. This DIO has been calculated to sufficient precision for aluminium [75][76][77][78][79][80][81][82], Mu2e's first target, but not for other nuclei. Ref.…”

Bound muon decay spectrum in the leading logarithmic accuracy

“…In the case of the bound muon, even O (α) effects are known only in a limited range of electron energies. Radiative corrections near the top of the electron spectrum in the free muon decay (E e ∼ mµ 2 ) were evaluated in [13] by convoluting the O (α) free-muon spectrum with the so-called shape function [14], reconciling TWIST results [1] with quantum electrodynamics. This approach had been developed in the heavy quark effective theory to describe decays of B-mesons [15,16] using factorization theorems.…”