QCD Sum Rules for the Isospin-Breaking Axial Correlator with Correct Chiral Behavior

Abstract

We revisit the QCD sum-rule treatment of the isospin-breaking axial correlator in light of the recent claim that a previous treatment produced results incompatible with known chiral constraints. The source of the error in the previous analysis is identified, and a corrected version of the sum-rule treatment obtained. It is then shown that, using input from chiral perturbation theory, one may use the resulting sum rule to extract information on the leading chiral behavior of isospin-breaking parameters associated with the coupling of excited pseudoscalar resonances to the axial currents. A rather accurate extraction is possible for the case of the eta'. Demanding stability of the sum-rule analysis also allows us to improve the upper bound on the fourth-order low-energy constant, L_7.