NNLO low-energy constants from flavor-breaking chiral sum rules based on   hadronic tau-decay data
  Using spectral data from non-strange and strange hadronic tau decays, flavor-breaking chiral sum rules involving the flavor ud and us current-current two-point functions are constructed and used to determine the SU(3) NNLO low-energy constant combinations C_{61}^r, C_{12}^r+C_{61}^r+C_{80}^r and C_{12}^r-C_{61}^r+C_{80}^r. The first of these determinations updates the results of an earlier analysis by Durr and Kambor, while the latter two are new. The error on the C_{12}^r+C_{61}^r+C_{80}^r is particularly small. Comparisons are made to model estimates for these quantities. The role of the third combination in significantly improving the determination of the NLO low-energy constant L_{10}^r from NNLO analyses of the flavor ud V-A correlator is also highlighted. 
M. Golterman, K. Maltman and S. Peris
hep-ph hep-ex hep-lat