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

Abstract

We determine the O(α) correction to the energy spectrum of electrons produced in the decay of muons bound in atoms. We focus on the high-energy end of the spectrum that constitutes a background for the muon-electron conversion and will be precisely measured by the upcoming experiments Mu2e and COMET. The correction suppresses the background by about 15%.

Bound muon decay spectrum in the leading logarithmic accuracy

“…1. For a 1 MeV signal window near the endpoint, we obtain a 12% reduction of the number of DIO events, consistent with [17].…”

“…Should the DIO spectrum be needed for electron energies closer to the endpoint, we recommend using eq. (2) in [17], where soft photons have been exponentiated.…”

“…[17] provided the correction to the leading term of the spectrum expanded in Zα: δ VP,(Zα) 5 = 2.9%. The difference with δ VP is caused by higher orders in Zα, estimated as minus 20% of the leading (Zα) 5 term [17]. As a check, we have compared our results with the spectrum measured by TWIST [1].…”

“…We use them to tabulate the DIO spectrum for aluminum including leading logarithmic corrections; see supplemental material [36]. This choice is further justified by the muon DIO amplitude near the endpoint being proportional to the elastic scattering amplitude [17]. To quantify the dependence of the error on the electron energy, we approximate the one-sigma boundaries (the shaded region in Fig.…”

“…Fortunately, the highest energy endpoint of the DIO spectrum (E e ∼ m µ ) offers a different simplification: one * szafron@ualberta.ca can expand in the number of photons exchanged with the nucleus, parameterized by Zα where Z is the proton number of the nucleus (for aluminum, Z = 13). Radiative corrections in the endpoint region have been evaluated in [17]. It is still unknown how to compute full radiative corrections for intermediate electron energies [18].…”