-Resonance and convergence of chiral perturbation theory
The dimensionless parameter′ = M2/(16π2F2), where F is the pion decay constant in the chiral limit and M is the pion mass at leading order in the quark mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter -resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of . We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the -regime and the p-regime. However,′ . 0.002 is necessary before 1-loop chiral perturbation theory predicts the data within 1%. However, for′ > 0.0035 the data begin to deviate qualitatively from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light -resonance in our model. Our findings may be useful for lattice QCD studies.
