ππ interaction in the ρ channel in finite volume

Abstract

The aim of this paper is to investigate an efficient strategy that allows one to obtain ππ phase shifts and ρ meson properties from QCD lattice data with high precision. For this purpose we evaluate the levels of the ππ system in the ρ channel in finite volume using chiral unitary theory. We investigate the dependence on the π mass and compare this with other approaches which use QCD lattice calculations and effective theories. We also illustrate the errors induced by using the conventional Lüscher approach instead of a more accurate one that was recently developed that takes into account exactly the relativistic two-meson propagators. Finally, we make use of this latter approach to solve the inverse problem, getting ππ phase shifts from "synthetic" lattice data, providing an optimal strategy and showing which accuracy is needed in these data to obtain the ρ properties with a desired accuracy. © 2013 American Physical Society.