Low-energy constants and condensates from ALEPH hadronic $\tau$ decay data

Abstract

We determine the NLO chiral low-energy constant $L_{10}^r$, and combinations $C_{12}^r\pm C_{61}^r+C_{80}^r$, $C_{13}^r-C_{62}^r+C_{81}^r$, $C_{61}^r$, and $C_{87}^r$, of the NNLO chiral low-energy constants incorporating recently revised ALEPH results for the non-strange vector ($V$) and axial-vector ($A$) hadronic $\tau$ decay distributions and recently updated RBC/UKQCD lattice data for the non-strange $V-A$ two-point function. In the $\overline{\mathrm{MS}}$ scheme, at renormalization scale $\mu =770MeV$, we find $L_{10}^r=-0.00350(17)$, $C_{12}^r+C_{61}^r+C_{80}^r=0.00237(16){GeV}^{-2}$, $C_{12}^r-C_{61}^r+C_{80}^r=-0.00056(15){GeV}^{-2}$, $C_{13}^r-C_{62}^r+C_{81}^r=0.00046(9){GeV}^{-2}$, $C_{61}^r=0.00146(15){GeV}^{-2}$, and $C_{87}^r=0.00510(22){GeV}^{-2}$. With errors here at or below the level expected for contributions of yet higher order in the chiral expansion, the analysis exhausts the possibilities of what can be meaningfully achieved in an NNLO analysis. We also consider the dimension six and dimension eight coefficients in the operator product expansion in the $V-A$ channel.

16 pages, revtex

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• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• The case for duality violations in the analysis of hadronic $\tau$ decays
• Low-energy constant $L_{10}$ in a two-representation lattice theory
• Towards tests of quark-hadron duality with functional analysis and spectral function data
• Determination of the NNLO low-energy constant $C_{93}$
• Effective Field Theories and Lattice QCD
• Confronting hadronic tau decays with non-leptonic kaon decays
• Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes
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• ChPT parameters from tau-decay data