L_{10}^r$ From a Combined NNLO Lattice, Continuum Analysis of the Light Quark V-A Correlator

A combination of lattice and continuum data for the light-quark V-A correlator, supplemented by results from a chiral sum-rule analysis of the flavor-breaking flavor $ud$-$us$ V-A correlator difference, is shown to make possible a high-precision NNLO determination of the renormalized NLO chiral low-...

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Hauptverfasser: Boyle, P. A, Del Debbio, L, Garron, N, Hudspith, R. J, Kerrane, E, Maltman, K, Zanotti, J. M
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Hudspith, R. J
Kerrane, E
Maltman, K
Zanotti, J. M
description A combination of lattice and continuum data for the light-quark V-A correlator, supplemented by results from a chiral sum-rule analysis of the flavor-breaking flavor $ud$-$us$ V-A correlator difference, is shown to make possible a high-precision NNLO determination of the renormalized NLO chiral low-energy constant $L_{10}^r$. Key to this determination is the ability to simultaneously fix the two combinations of NNLO low-energy constants also entering the analysis. With current versions of the strange hadronic $\tau$ branching fractions required as input to the flavor-breaking V-A sum rule, we find $L_{10}^r(m_\rho ) = -0.00346(29)$. This represents both the best current precision for $L_{10}^r$, and the first NNLO determination having all errors under full control.
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title L_{10}^r$ From a Combined NNLO Lattice, Continuum Analysis of the Light Quark V-A Correlator
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