Anomalous Evolution of the Gottfried Sum

We discuss nonperturbative QCD evolution of nonsinglet nucleon structure functions, with particular application to the Gottfried sum. We show that the coupling of the quark partons to bound state mesons leads to nonperturbative contributions to the Altarelli– Parisi equations which, due to the axial anomaly, result in a strong scale dependence of nonsinglet structure functions for values of Q around the nucleon mass scale. We compute specifically the evolution of the first moment of the quark distribution, and find that it is ⋆ Address from October 1993 (RDB) and December 1993 (SF): Theory Division, CERN, CH– 1211 Genève 23, Switzerland. sufficient to explain recent experimental data which indicate a violation of the Gottfried sum rule. Submitted to: Nuclear Physics B 1. Violation of the Gottfried Sum Rule In the wake of the furore over the EMC measurement [1] of quark polarized structure functions, experimental results from the NMC[2] for the Gottfried sum again appear to be in contradiction with theoretical expectations. More specifically, the NMC measure the ratio of the cross–sections for unpolarized deep–inelastic scattering from deuterium and hydrogen targets. The ratio of structure functions F d 2 (x,Q ) / F p 2 (x,Q ) is extracted in the range 0.004 ≤ x ≤ 0.8 at Q = 4 GeV. Extrapolating to small x using Regge behaviour, and assuming further that the neutron structure function is just F 2 = 2F d 2 − F p 2 allows a determination of the Gottfried sum, defined as