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

TL;DR

This paper determines the QCD chiral order parameters L_10 and C_87 from precise tau decay data using QCD properties and chiral perturbation theory, providing accurate low-energy constants at different orders.

Contribution

It provides the first precise determination of L_10 and C_87 from tau decay data, including two-loop contributions, improving understanding of low-energy QCD parameters.

Findings

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

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} at order p^6

Values of ar l_5 in SU(2) chiral theory at different orders

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^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}. 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.