Low-energy constants and condensates from the tau hadronic spectral functions

TL;DR

This paper uses tau decay spectral data to determine low-energy constants and condensates in chiral perturbation theory, providing a self-consistent analysis of quark-hadron duality violations and operator product expansion contributions.

Contribution

First to employ a fully self-consistent model for quark-hadron duality violations in determining low-energy constants from tau decay data.

Findings

Determined effective low-energy constants L_10^eff and C_87^eff.

Assessed the accuracy of two-loop chiral perturbation theory for bPi_{V-A}(Q^2).

Estimated coefficients C_{6,V-A} and C_{8,V-A} for operator product expansion.

Abstract

We use results of fits to the OPAL spectral data, obtained from non-strange hadronic \tau decays, to evaluate the difference between the vector and axial current correlators, \Pi_{V-A}(Q^2). The behavior of \Pi_{V-A}(Q^2) near euclidean momentum Q^2=0 is used to determine the effective low-energy constants L_10^eff and C_87^eff related to the renormalized low-energy constants L_10^r and C_87^r in the chiral lagrangian. We also investigate how well two-loop chiral perturbation theory describes \Pi_{V-A}(Q^2) as a function of Q^2. This is the first determination of L_10^eff and C_87^eff to employ a fully self-consistent model for the violations of quark-hadron duality in both the vector and axial channels. We also discuss the values of the coefficients C_{6,V-A} and C_{8,V-A} governing the dimension six and eight contributions to the operator product expansion representation of \Pi_{V-A}(Q^2).