Correlator of topological charge densities at low q(2) in QCD: Connection with proton spin problem

The vacuum correlator of topological charge densities chi(q(2)) at low q(2) in QCD is discussed: its value chi(0) and first derivative chi'(0) at q(2) = 0 and the contributions of pseudoscalar quasi-Goldstone bosons to chi(q2 ) at low q(2). The QCD sum rule [1], giving the connection of chi'(0) (for massless quarks) with the part of the proton spin Sigma, carried by u, d, s quarks, is presented. From the requirement of self-consistence of the sum rule the values of chi'(0) and Sigma were found. The same value of chi'(0) follows also from the experimental data on Sigma. The contributions of pi a nd eta to chi(q(2)) are calculated based on low-energy theorems. In such ca lculations the pi - eta mixing, expressed in terms of quark mass ratios, is of importance.