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

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) = -(5.22pm 0.06)10^{-3}. Including in the analysis the two-loop (order p^6) contributions, we get L_10^r(M_rho) = -(4.06pm 0.39)10^{-3} and C_87^r(M_rho) = (4.89pm 0.19)10^{-3}GeV^{-2}. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value overline l_5 = 13.30 pm 0.11 at order p^4, and overline l_5 = 12.24 pm 0.21 at order p^6.

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

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.