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The isospin-breaking correlator of the product of flavor octet vectorcurrents, $V^3_\mu$ and $V^8_\nu$, $\Pi^{38}_{\mu\nu}(q^2)$ is computed tonext-to-next- to-leading (two-loop) order in Chiral Perturbation Theory. Largecorrections to both the magnitude and $q^2$-dependence of the one-loop resultare found, and the reasons for the slow convergence of the chiral series forthe correlator given. The two-loop expression involves a single ${\cal O}(q^6)$counterterm, present also in the two-loop expressions for$\Pi^{33}_{\mu\nu}(q^2)$ and $\Pi^{88}_{\mu\nu}(q^2)$, which countertermcontributes a constant to the scalar correlator $\Pi^{38}(q^2)$. Thefeasibility of extracting the value of this counterterm from other sources isdiscussed. Analysis of the slope of the correlator with respect to $q^2$ usingQCD sum rules is shown to suggest that, even to two-loop order, the chiralseries for the correlator may not yet be well-converged.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Vector current correlator 〈0|T(Vμ3V<…