Remarks on the radiative corrections of order α2 to muon decay and the determination of Gμ

Abstract

Abstract We discuss several theoretical aspects of the study of the radiative corrections to the total decay probability P in μ-decay. On the basis of the theorem on cancellation of mass singularities, we obtain by a simple argument, that part of the radiative corrections of order α2 to P which contains mass singularities (i.e. terms which diverge in the mathematical limit me → 0) in an expansion in powers of the renormalized charge. We also state a theorem on the effect of the finite electron mass on the radiative corrections of order α. We then discuss an exponentiation method recently applied to study the corrections to P. We show by direct calculation that the method, as presently implemented, is ambiguous and that it leads, to order α2, to a violation of the conclusions obtained on the basis of the theorem on mass singularities. Finally we give what we consider to be the best value presently available for Gμ in the framework of the local V-A theory, and briefly discuss the expected order of magnitude of the theoretical error.