Connecting physical resonant amplitudes and lattice QCD

Abstract

We present a determination of the isovector, P-wave ππ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using mπ=236MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at mπ=140MeV. The scattering phase shift is found to agree with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a ρ-resonance pole at Eρ=[755(2)(1)(2002)−i2129(3)(1)(71)] MeV. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.