Electromagnetic Mass Difference of Hadrons and the Parton Model

Abstract

The parton model is used to calculate the forward virtual Compton scattering amplitude off hadrons in the deep inelastic region. Inserting it into the Cottingham formula for the electromagnetic mass difference of hadrons, we obtain the vanishing deep-inelastic contribution to the .:11=2 mass difference and the logarithmically divergent contribution to the .:11;,1 mass difference, the sign of which depends on the choice of specific models for the part on : the quark, quartet, two-triplet and three-triplet models. The quartet-type model proposed by Namiki and Tanaka seems to be preferable. § I. Introduction and summary There has been a great deal of controversy on the electromagnetic mass difference of hadrons, especially on the p-n mass difference. In his beautiful paper, HararP) observed on the basis of the Regge-pole theory that the forward virtual Compton scattering amplitude for the I= 2 t-channel state satisfies an unsubtracted dispersion relation in the photon energy while that for the· I= 1 t­ channel state requires a once-subtracted dispersion relation. He claimed that the subtraction term in the virtual Compton amplitude for the I= 1 t-channel state is responsible for reversing the wrong sign of the pole contribution in the Cottingham formula 2 ) for the L1I=1 mass difference, e.g. p-n, .s+-.s-, 8°-E-, K+- K 0 • The unnecessity of the subtraction term in the virtual Compton am­ plitude for the I= 2 t-channel state supports the fact that the JI = 2 mass differ­ ence, e.g. _s+ + .s-- 2.2°, n+- rc 0 can be accounted for only by the pole contribution in the Cottingham formula. Although Harari's argument is attractive, one can not draw any conclusions on the sign of the JI = 1 mass difference unless one can estimate the contribution of the subtraction term to the mass difference. In ,the hope of getting some information on the subtraction pi_ece ·in the mass differ­ ence, several attempts have been made to estimate the Regge asymptote of the virtual Compton amplitude by using the finite energy sum rules.