From hadronic tau decays to the chiral couplings L_10 and C_87

TL;DR

This paper uses sum rule analysis of tau-decay data to determine low-energy constants in chiral perturbation theory, providing precise values for L10 and C87 at different orders.

Contribution

It presents a novel sum rule analysis incorporating p^6 contributions to accurately extract chiral low-energy constants from tau decay data.

Findings

L10(M_rho) = -(5.22±0.06)×10^-3 at order p^4

L10(M_rho) = -(4.06±0.39)×10^-3 and C87(M_rho) = (4.89±0.19)×10^-3 GeV^-2 including p^6 terms

Enhanced precision in low-energy constant determination from tau decay data

Abstract

A sum rule analysis of the hadronic tau-decay data can be used to determine the low-energy constants L10(mu) and C87(mu). These constants are QCD chiral-order parameters, which appear at order p^4 and p^6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p^4 we obtain L10(M_rho) = -(5.22\pm 0.06)10^-3. Including in the analysis the order p^6 contributions, we get L10(M_rho) = -(4.06\pm 0.39)10^-3 and C87(M_rho) = (4.89\pm 0.19)10^-3 GeV^-2.