Determination of the ‘lepton-charge violating’ coupling constants in muon decay

Abstract

Muon decay, without requiring conservation of the lepton charge, is examined. The coupling constants occuring in the terms of the interaction Hamiltonian which can give rise to a pair of identical neutrinos (or antineutrinos) are reffered to as the lepton-charge-violating coupling constants. Using the predicted V-A values for four decay parameters (which are close to the experimental values) we show that only four coupling constants, viz., g V and g A of the ordinary theory and g A and g ̂ A of the lepton-charge violating interactions remain undertermined. Further, only the combination |g V | 2+|g A | 2+2| g A | 2+2| g ̂ A | 2 can be measured. The further assumption of the two-component theory for one of the decay neutrinos gives uniquely the V-A theory ( g A = g ̂ A = 0 and g V = −g A ). Allowing for the experimental uncertainties, lepton-charge-violating scalar and pseudoscalar interactions of about the same order of magnitude as the usual scalar and pseudoscalar interactions cannot be excluded. The significance of future measurements of η′, one of the decay parameters for radiative muon decay, for finding upper limits to the scalar, pseudoscalar and tensor interactions is also discussed.