Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays

Understand

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^r(M_rho) and C_87^r(M_rho).

• These two low-energy constants 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 L_10^r(M_rho) = -(5.22\pm 0.06)10^{-3}.
• Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06\pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89\pm 0.19)10^{-3}GeV^{-2}.