Gonzalez-Alonso, M., Pich, A., & Prades, J. (2010). Violation of quark-hadron duality and spectral chiral moments in QCD. Phys. Rev. D, 81(7), 074007–10pp.
Abstract: We analyze the spectral moments of the V – A two-point correlation function. Using all known short-distance constraints and the most recent experimental data from tau decays, we determine the lowest spectral moments, trying to assess the uncertainties associated with the so-called violations of quark-hadron duality. We have generated a large number of acceptable spectral functions, satisfying all conditions, and have used them to extract the wanted hadronic parameters through a careful statistical analysis. We obtain accurate values for the chi PT couplings L-10 and C-87, and a realistic determination of the dimension six and eight contributions in the operator product expansion, O-6 = (-5.4(-1.6)(+3.6)) . 10(-3) GeV6 and O-8 = d(-8.9-(12.6)(7.4+)) 10(-3) GeV8, showing that the duality-violation effects have been underestimated in previous literature.
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Gonzalez-Alonso, M., Pich, A., & Rodriguez-Sanchez, A. (2016). Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data. Phys. Rev. D, 94(1), 014017–14pp.
Abstract: We analyze the lowest spectral moments of the left-right two-point correlation function, using all known short-distance constraints and the recently updated ALEPH V – A spectral function from tau decays. This information is used to determine the low-energy couplings L-10 and C-87 of chiral perturbation theory and the lowest-dimensional contributions to the operator product expansion of the left-right correlator. A detailed statistical analysis is implemented to assess the theoretical uncertainties, including violations of quark-hadron duality.
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