Determination of the chiral couplings L10 and C87 from semileptonic τ decays

Abstract

Using recent precise hadronic τ-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 L10r(Mρ) and C87r(Mρ). These two low-energy constants appear at order p4 and p6, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p4 we obtain L10r(Mρ)=-(5.22±0.06)×10-3. Including in the analysis the two-loop (order p6) contributions, we get L10r(Mρ)=-(4.06±0.39)×10-3 and C87r(Mρ)=(4.89±0.19)×10-3 GeV-2. In the SU(2) chiral effective theory, the corresponding low-energy coupling takes the value l̅ 5=13.30±0.11 at order p4, and l̅ 5=12.24±0.21 at order p6.