@article{bb512ac0f78d493ab63eb6fb17cb6fca, title = "Combined Lattice and Continuum Analysis of the Light Quark $V-A$ Correlator at NNLO in ChPT", abstract = "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.", keywords = "hep-ph, hep-lat", author = "{A. Boyle}, P. and {Del Debbio}, L. and N. Garron and {J. Hudspith}, R. and E. Kerrane and K. Maltman and {M. Zanotti}, J.", note = "7 pages, 2 figures. Prepared for the proceedings of the 31st International Symposium on Lattice Field Theory, July 29-August 3, 2013, Mainz, Germany; 31st International Symposium on Lattice Field Theory - LATTICE 2013 ; Conference date: 29-07-2013 Through 03-08-2013", year = "2013", month = nov, day = "2", language = "English", volume = "2013", journal = "Proceedings of Science", issn = "1824-8039", publisher = "Sissa Medialab Srl", number = "LATTICE 2013", }