We test the convergence property of the chiral perturbation theory (ChPT) using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which realizes exact chiral symmetry at finite lattice spacing. By comparing various expansion prescriptions, we find that the chiral expansion is well saturated at the next-to-leading order (NLO) for pions lighter than $sim$450 MeV. Better convergence behavior is found in particular for a resummed expansion parameter $xi$, with which the lattice data in the pion mass region 290$sim$750 MeV can be fitted well with the next-to-next-to-leading order (NNLO) formulae. We obtain the results in two-flavor QCD for the low energy constants $bar{l}_3$ and $bar{l}_4$ as well as the pion decay constant, the chiral condensate, and the average up and down quark mass.
Download