Chiral low-energy constants L_10 and C_87 from hadronic tau decays

TL;DR

This paper determines precise values of the QCD chiral low-energy constants L_10 and C_87 using recent tau decay data, QCD principles, and chiral perturbation theory, improving understanding of low-energy QCD parameters.

Contribution

The paper provides the first accurate extraction of L_10 and C_87 from tau decay data using a combination of QCD techniques and chiral perturbation theory, including order p^6 corrections.

Findings

L_10^r(M_rho) at order p^4: -(5.22±0.06)×10^-3

L_10^r(M_rho) at order p^6: -(4.06±0.39)×10^-3

C_87^r(M_rho): (4.89±0.19)×10^-3 GeV^-2

Abstract

Using recent precise hadronic tau-decay data on the V-A spectral function and general properties of QCD such as analyticity, the operator product expansion and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L_10 and C_87. At order p^4 we obtain L_10^r(M_rho)=-(5.22+-0.06)10^-3, whereas at order p^6 we get L_10^r(M_rho)=-(4.06+-0.39)10^-3 and C_87^r(M_rho) = (4.89+-0.19)10^-3 GeV^-2.