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Using recent precise hadronic tau-decay data on the V-A spectral function,and general properties of QCD such as analyticity, the operator productexpansion and chiral perturbation theory, we get accurate values for the QCDchiral order parameters L_10^r(M_rho) and C_87^r(M_rho). These two low-energyconstants appear at order p^4 and p^6, respectively, in the chiral perturbationtheory 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}. In the SU(2) chiral effective theory, thecorresponding low-energy coupling takes the value \overline l_5 = 13.30 \pm0.11 at order p^4, and \overline l_5 = 12.24 \pm 0.21 at order p^6.

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