Pion and Nucleon Structure Functions nearx=1

Abstract

In a colored-quark and vector-gluon model of hadrons we show that a quark carrying nearly all the momentum of a nucleon (x f':j 1) must have the same helicity as the nucleon;consequently vWt/vW/-.f as x-1, not .j. as might naively have been expected. Furthermore as x-1, vW 2~~"~ (1-x) 2 and (aL/aT) .. ~J.1~-2 (1-x)-2 +0(g 2 ); the resulting angular dependence for e+e--h±+x is consistent with present data and has a disti,nctive form which can be easily tested when better data are available.There have been two significant paradoxes associated with the interpretation of electron-hadron scattering at large q 2 in terms of quarks:where x=-q 2 /(2q·p), appears to reflect the underlying three-quark structure of the proton at short distances, 1 that same three-quark struc-. ture with the simple dynamics that controls short-distance processes would naively appear to lead to the prediction vW 2 n/vW/-j as x-1, contrary to observation. 2 Furthermore, while for Q 2 ~ 15 GeV 2 the colored-quark model gives the correct value of the famous ratio R =a(e+e--hadrons )/ a(e + e--fJ. + fJ.-), that same model has been thought to predict a (1 +cos 2 8) angular distribution for hadrons having large x=2IPI /Q. Instead, in that same Q 2 range the distribution is roughly isotropic. 3 We show here that the above paradoxes are products of the naive arguments:In fact, when the actual dynamics of the quarkgluon interaction are considered, the predictions are in good agreement with observations. The problem of calculating properties of structure functions is tractable, we believe, for large Q 2 and x"' 1 because in that kinematic configuration the quark which couples to the electromagnetic current necessarily has a very large invariant mass, even in the scaling limit. 4 A wave function in which one quark has. very large invariant mass can be generated from the "normal" wave fun~tion (in which the invariant mass of each quark is limited) by an interaction of the sort shown in Fig. 1, where the incoming quark lines are understood to be convoluted with the normal wave function. Since each propagator marked with a cross has a large invariant mass [p 2 -m 2 /(1-x), where m 2 is some characteristic mass or P 1. scale for the quarks], it is reasonable to imagine that the effective quark-gluon couplings displayed in Fig. 1 are small. 5 Thus we can use lowest-order perturbation theory to 1416 go from the normal to "exceptional" (one quark having large P 2 ) wave functions. We assume that (a) the normal wave function is sufficiently damped at large P 2 ' s that the convolution is dominated by the region in which the p 2 ' s of the incoming quarks are finite, and (b) the spin and SU(3) structure of the normal wave function are what one would have in a nonrelativistic quark model. With these two assumptions, 6 the x-1 properties of hadron structure functions are given to O(m 2 / q 2 ) by lowest-order perturbation theory in which the incoming quarks can be treated as free (Fig. 1), 7 the convolution with the wave function having no effect other than fi...

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