Chiral extrapolation beyond the power-counting regime

Abstract

Chiral effective field theory can provide valuable insight into the chiral physics of hadrons when used in conjunction with nonperturbative schemes such as lattice quantum chromodynamics (QCD). In this discourse, the attention is focused on extrapolating the mass of the $\ensuremath{\rho}$ meson to the physical pion mass in quenched QCD. With the absence of a known experimental value, this serves to demonstrate the ability of the extrapolation scheme to make predictions without prior bias. By using extended effective field theory developed previously, an extrapolation is performed using quenched lattice QCD data that extends outside the chiral power-counting regime. The method involves an analysis of the renormalization flow curves of the low-energy coefficients in a finite-range regularized effective field theory. The analysis identifies an optimal regularization scale, which is embedded in the lattice QCD data themselves. This optimal scale is the value of the regularization scale at which the renormalization of the low-energy coefficients is approximately independent of the range of quark masses considered. By using recent precision, quenched lattice results, the extrapolation is tested directly by truncating the analysis to a set of points above 380 MeV, while temporarily disregarding the simulation results closer to the chiral regime. This tests the ability of the method to make predictions of the simulation results, without phenomenologically motivated bias. The result is a successful extrapolation to the chiral regime.