Right-handed Electrons in Radiative Muon Decay

Electrons emitted in the radiative decay μ− → e−ν̄eνμγ have a significant probability of being right-handed, even in the limit me → 0. Such “wrong-helicity” electrons, arising from helicity-flip bremsstrahlung, contribute an amount α 4π Γ0 to the muon decay width (Γ0 ≡ G 2 Fm 5 μ/(192π )). We use the helicity-flip splitting function Dhf (z) of Falk and Sehgal (Phys. Lett. B 325, 509 (1994)) to obtain the spectrum of the right-handed electrons and the photons that accompany them. For a minimum photon energy Eγ = 10MeV (20MeV ), approximately 4% (7%) of electrons in radiative μ-decay are right-handed. It is usually thought that in V-A theory, electrons emitted in muon decay are purely left-handed, in the limit me → 0. This statement, however, is not true for electrons in the radiative decay μ− → e−ν̄eνμγ, where the photon is the result of inner bremsstrahlung. We show in this Letter that radiative muon decay contains a well-defined constituency of right-handed electrons, contributing an amount α 4π Γ0 (Γ0 ≡ G 2 Fm 5 μ/(192π )) to the decay width. We calculate the spectrum of these “wrong-helicity” electrons, and of the photons that accompany them. These spectra are compared with the unpolarized spectra, summed over electron helicities. This comparison provides a quantitative measure of the right-handed fraction and its distribution in phase space. The appearance of “wrong-helicity” electrons in the decay μ− → e−ν̄eνμγ, even in the limit me → 0, is a consequence of helicity-flip bremsstrahlung in quantum electrodynamics, a feature first noted by Lee and Nauenberg [1]. It was found that in the radiative scattering of electrons by a Coulomb field, the probability of helicity-flip (i.e. eL → eR or eR → eL) did not vanish in the limit me → 0. This unexpected result, in apparent contradiction to the naive expectation of helicity conservation in the me → 0 limit, arises from the fact, that the helicity-flip cross section for bremsstrahlung at small angles has the Preprint submitted to Elsevier Science 1 February 2008