Uncorrelated Two Pion Effects in the Superconvergent Dispersion Relation for the Nucleon Electromagnetic Form Factors

Abstract

We incorportate uncorrelated two pion effects in the superconvergent dispersion relations for the electromagnetic form factors of nucleon which have been proposed by us to synthesize the hadron physics in the low energy and the perturbative QCD in the high energy region. Inclusion of the uncorrelated two pion effects improves the result appreciably as compared with the previous calcula­ tion where the vector dominance is assumed for the low energy region. In the previous paper we investigated the elastic electromagnetic form factors of nucleons with recourse to the unsubtracted dispersion relations with the superconver­ gence conditions. 1) We were able to synthesize the hadron and quark systems in the following respect: The calculated form factors reproduce the result of vector domi­ nance model (VDM) in the low t region, t being the squared momentum transfer, ,and asymptotically they realize the prediction of the perturbative QCD. We shall call the paper, Ref. 1), I hereafter. Good agreement was obtained with the experimental data but we still had the following problems: First, the theoretical result for the electric form factor of proton becomes slightly larger than the experimental data in the low t region. Secondly, we must take the p meson mass mp much smaller than the experimental one; the best fit was obtained for mp;;::; 0.63 Ge V while experimentally it is 0.77 GeV. It is the purpose of this paper to solve the problems by taking into account the uncorrelated two pions in the superconvergent dispersion relations as we did in the analysis of low energy hadronic processes for which thep wave two pions contrib­ ute. 2 ),3) We break up the dispersion integral into three parts at t = A12 and.t = A22 as in 1. In the region 4,u2< t < A1 2 , ,u being the pion mass, the iso-vector absorptive parts are given in terms of the helicity amplitudes 7r7r-NN with] = 1 by using the formulae given in Ref. 2). For the iso-scalar parts the vector dominance is assumed with the (f) and ¢ mesons. The higher t regions are treated in the same way as was done in, I; for the intermediate region A12< t<Al the vector dominance is also-assumed witn; heavy vector bosons phenomenologically introduced. The absorptive parts in the high t region, A22< t, are taken so as to reproduce the asymptotic form factors derived via the perturbative QCD. 4 )