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
- Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, M3J 1P3 (CANADA)
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}}{sup 88}({ital q}{sup 2}), which counterterm contributes a constant to the scalar correlator {Pi}{sup 38}({ital q}{sup 2}), defined by {Pi}{sub {mu}{nu}}{sup 38}({ital q}{sup 2}){equivalent_to}({ital q}{sub {mu}}{ital q}{sub {nu}}{minus}{ital q}{sup 2}{ital g}{sub {mu}{nu}}) {Pi}{sup 38}({ital q}{sup 2}). The feasibility of extracting the value of this counterterm from other sources is discussed. Analysis of the slope of the correlator with respect to {ital q}{sup 2} 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 {ital O}({ital q}{sup 8}) contributions discussed. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 279176
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 5 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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