Vector current correlator 〈0|T(Vμ³ Vν⁸) |0〉 to two loops in chiral perturbation theory

Abstract

The isospin-breaking correlator of the product of flavor octet vector currents, Πμν³⁸(q²)= i∫d4x exp(iq⋅x)〈0|T(Vμ³ Vν⁸) |0〉, is computed to next-to-next-to-leading (two-loop) order in chiral perturbation theory. Large corrections to both the magnitude and q² dependence of the one-loop result are found, and the reasons for the slow convergence of the chiral series for the correlator given. The two-loop expression involves a single O(q6) counterterm, present also in the two-loop expressions for Πμν³³(q²) and Πμν⁸⁸(q²), which counterterm contributes a constant to the scalar correlator Π³⁸(q²), defined by Πμν³⁸(q²≡(qμqν-q2gμν) Π3⁸(q²). The feasibility of extracting the value of this counterterm from other sources is discussed. Analysis of the slope of the correlator with respect to q² using QCD sum rules is shown to suggest that, even to two-loop order, the chiral series for the correlator may not yet be well converged, and the physical origins of possible important O(q8) contributions discussed.