We propose a simple model for the structure functions characterizing deep-inelastic leptoproduction off nucleons. Our approach adapts the quark-parton model to include scaling violations predicted in asymptotically free gauge theories. With the normalization of I. w, f$ed by data at essentially two values of Q ', we are able to predict v Wz over the remaining, large experimental range. The agreement with the data is good even down to quite low values of Q (Q --1 GeV2). Given our model for v UJ, and a model for F,, we obtain unique predictions for 2MW, and hence for R = ~-~/ r r , .The agreement of the former with experiment is as good as in the case of v W,. The predictions for R while still somewhat low at small x are substantially better, especially at high x , Lhan those deduced previously in approaches based on asymptotically free gauge theories.
I, INTRODUCTIONThe past ten years have seen the emergence of deep-inelastic lepton-hadron scattering a s one of the major tools for probing the structure of the nucleon and unraveling the nature of strong interactions. Confirming a prediction of Bjorken,' electroproduction experiments2 revealed an apparent scaling behavior of the structure functions. This led to the formulation of the "naive quark-parton model" (QPM),3 in which the exchanged virtual phpton appears to interact with quasifree pointlike objects in the nucleon. The resulting dimensionless structure functions were then related by the CallanGross sum rule.4More recent experimental work,=e6 however, using both electrons and muons, has disclosed sizable deviations from scaling. Neutrino scattering7 confirms the QPM picture, and now has sufficient resolving power to exhibit scale-breaking in a conclusive fashion. The uncertainties which subsist result both from the large imprecision associated with neutrino experiments up to now, and from their sensitivity to threshold effects and to the number of quarks, o r flavors, that the W boson can couple to.Attemptsa to understand Bjorken scaling in the framework of field theory, spurred by the (then) recent developments in non-Abelian gauge theories, have generated unexpected insight into the very structure of the strong interactions. What has emerged is a picture (quantum chromodynamics, o r QCD) where colored triplets of quarks interact with an octet of vector gluons. Provided that the number of flavors does not exceed a certain value [16 if the color gauge group is SU(3)], the quarkgluon coupling constant a, goes to zero in the limit of infinite-momentum transfer g2. Thus, this asymptotically free gauge theory (AFGT) can explain exact scaling a t infinite gZ. In addition, it predicts logarithmic deviations from scaling in the finite-&' region, which in principle can be calculated to arbitrary order in a,.AFGT's a r e not unique in predicting scale violat i o n~,~ but calculating such effects in other possible models and theories of the strong interactions involves assumptions which a r e not necessary in AFGT's. For instance, in non-asymptotically -free field theo...
