Combined NNLO lattice-continuum determination of Lr₁₀

Abstract

The renormalized next-to-leading-order chiral low-energy constant, Lr10, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor ud V−A correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of ud and us V−A correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for Lr10. Using the results of the flavor-breaking chiral V−A sum rule obtained with current versions of the strange hadronic τ branching fractions as input, we find Lr10(mρ)=−0.00346(32). This result represents the first NNLO determination of Lr10, having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.