The Mixed - Isospin Vector Current Correlator in ChiralPerturbation Theory and QCD

The mixed-isospin vector current correlator, h0jT(V V !)j0i is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modiication of previous analyses necessitated by the observation that those analyses produce forms of the correlator that fail to be dominated, near q 2 = 0, by the most nearby singularities. Inclusion of contributions associated with the meson rectify this problem. The resulting sum rule t provides evidence for a signiicant direct ! ! coupling contribution in e + e ? ! + ?. It is also pointed out that results for the q 2-dependence of the correlator cannot be used to provide information about the (oo-shell) q 2-dependence of the oo-diagonal element of the vector meson propagator unless a very speciic choice of interpolating elds for the vector mesons is made. The results for the value of the correlator near q 2 = 0 in ChPT are shown to be more than an order of magnitude smaller than those extracted from the sum rule analysis and the reasons why this suggests slow 1 convergence of the chiral series for the correlator given.