## Vector current correlator {l_angle}0{parallel}{ital T}({ital V}{sub {mu}}{sup 3}{ital V}{sub {nu}}{sup 8}){parallel}0{r_angle} to two loops in chiral perturbation theory

The isospin-breaking correlator of the product of flavor octet vector currents, {Pi}{sub {mu}{nu}}{sup 38}({ital q}{sup 2})= {ital i}{integral}{ital d}{sup 4}{ital x}exp({ital iq}{center_dot}{ital x}){l_angle}0{parallel}{ital T}[{ital V}{sub {mu}}{sup 3} ({ital x}){ital V}{sub {nu}}{sup 8}(0)]{parallel}0{r_angle}, is computed to next-to-next-to-leading (two-loop) order in chiral perturbation theory. Large corrections to both the magnitude and {ital q}{sup 2} 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 {ital O}({ital q}{sup 6}) counterterm, present also in the two-loop expressions for {Pi}{sub {mu}{nu}}{sup 33}({ital q}{sup 2}) and {Pi}{sub {mu}{nu}}{supmore »