Comparison of Chiral Perturbation Theory and QCD Sum Rule Results for Pseudoscalar Isoscalar-Isovector Mixing

Abstract

The forms of the neutral, non-strange pseudoscalar propagator matrix and mixed axial current correlator, $\lngle0|T(A_\mu^3 A_\nu^8)|0\rangle$, are discussed at next-to-leading (one-loop) order in chiral perturbation theory, and the results compared to those obtained using QCD sum rules. This comparison provides a check of the truncations employed in the sum rule treatment of the current correlator. Values for the slope of the correlator with $q^2$ in the two approaches are found to differ by more than an order of magnitude and the source of this discrepancy is shown to be the incorrect chiral behavior of the sum rule result.