To Two Loops in Chiral Perturbation Theory ADP - 95 - 27 / T 181 hep - ph / 9504404

The isospin-breaking correlator of the product of flavor octet vector currents, Π38 μν(q 2) = i ∫ d4x exp(iq.x) < 0|T (V 3 μ (x)V 8 ν (0))|0 >, is computed to next-tonext-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 Π33 μν(q 2) and Π88 μν(q 2), which counterterm contributes a constant to the scalar correlator Π38(q2), defined by Π38 μν(q 2) ≡ (qμqν − qgμν)Π(q). 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. 11.55.Hx, 12.39.Fe, 14.40.Cs, 24.85.+p Typeset using REVTEX 1