A critical analysis of the electromagnetic mass shift problem in QCD

Abstract

The paper analyzes the electromagnetic quark mass shift problem in the framework of QCD and concludes with a physically appealing sum rule for the proton-neutron mass difference, in which the contribution from the divergent part of the photon loop has the right sign, after it has been renormalized. The paper reconciles the conflicting conclusions reached by respectively using the operator product expansion and the Dyson equations. In a recent discussion based on the latter special significance was given to the number of flavours n f > 11, for which by choosing the ordering of integration and summation naturally dictated by iteration of the Dyson equation, the electromagnetic mass shift comes out to be finite with the correct sign for m u − m d. We show by using dimensional regularization and minimal subtraction for renormalization group improved Feynman graphs one obtains the same result independent of the number of flavours.