Some Difficulties in the Field-Theoretic Approach to the Proton-Neutron Mass Difference

SOme consequences of a manifest lack of gauge-invariance in the usual field-theoretic approach to the calculation of the proton-neutron mass difference are pointed out. In particular, it is shown that the assumption Z = 0 (where Z is the strong wavefunction renormalization constant) is inessential to this problem of gauge-dependence. A pracatical calculation of 6M = M Mn, assuming Z = 0 and relying on the method P of low-mass dominance of Drell and Pagels, is carried out. The cutoff for this calculation, h* = 3.6 for (g*/&) = 15, is determined by requiring that Z = 0 be satisfied O(g*). If we accept the possibility that the prescription adopted by Bassetto and Paccanoni (BP) for extracting a gauge-independent result has some basis, then we find, on including the effects of the anomalous nucleon moments, that 6M = .0.4 MeV, in rough agreement with their earlier result. However, inclusion of the vertex corrections O(a), which are neglected by BP, leads to the unsatisfactory result 6M = f 0.8 MeV.