The Mixed Vector Current Correlator <0|T(V^3_μV^8_ν)|0> To Two Loops in Chiral Perturbation Theory

Abstract

The isospin-breaking correlator of the product of flavor octet vector currents, $V_{\mu }^3$ and $V_{\nu }^8$, ${\Pi }_{\mu \nu }^{38}(q^2)$ is computed to next-to-next- to-leading (two-loop) order in Chiral Perturbation Theory. Large corrections to both the magnitude and $q^2$-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 $\mathcal{O}(q^6)$ counterterm, present also in the two-loop expressions for ${\Pi }_{\mu \nu }^{33}(q^2)$ and ${\Pi }_{\mu \nu }^{88}(q^2)$, which counterterm contributes a constant to the scalar correlator ${\Pi }^{38}(q^2)$. The feasibility of extracting the value of this counterterm from other sources is discussed. Analysis of the slope of the correlator with respect to $q^2$ 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.

32 pages, uses REVTEX and epsfig.sty with 7 uuencoded figures. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-27.T181.ps

References in corpus (6)

• Chiral perturbation theory
• Extension of the Chiral Perturbation Theory Meson Lagrangian to Order $P^6$
• Low-Energy Photon-Photon Collisions to Two-Loop Order
• Two-Loop Analysis of Vector Current Propagators in Chiral Perturbation Theory
• Field Transformations and the Classical Equation of Motion in Chiral Perturbation Theory
• The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum Rules

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• Two-loop Analysis of Axialvector Current Propagators in Chiral Perturbation Theory
• Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory
• Inverse-Moment Chiral Sum Rules
• The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum Rules
• NNLO low-energy constants from flavor-breaking chiral sum rules based on hadronic tau-decay data
• A ChPT estimate of the strong-isospin-breaking contribution to the anomalous magnetic moment of the muon
• Isospin-Breaking Vector Meson Decay Constants From Continuous Families of Finite Energy Sum Rules
• Isospin Breaking and $\omega$->$\pi \pi$ Decay
• Isospin Breaking Effects in the Extraction of Isoscalar and Isovector Spectral Functions From $e^{+}{e}^{-}\to hadrons$
• On extracting the rho-omega mixing amplitude from the pion form-factor
• Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes