The pion-pion Interaction in the rho Channel in Finite Volume

TL;DR

This paper develops an improved method to extract pi-pi phase shifts and rho meson properties from lattice QCD data, emphasizing the importance of relativistic effects and error analysis for precise results.

Contribution

It introduces a refined approach using relativistic two-meson propagators to accurately determine rho meson properties from finite volume lattice data.

Findings

Relativistic approach improves phase shift extraction accuracy.

Errors from conventional Luscher method can be significant.

Optimal data precision is identified for reliable rho property determination.

Abstract

The aim of this paper is to investigate an efficient strategy that allows to obtain pi-pi phase shifts and rho meson properties from QCD lattice data with high precision. For this purpose we evaluate the levels of the pi-pi system in the rho channel in finite volume using chiral unitary theory. We investigate the dependence on the pi mass and compare with other approaches which use QCD lattice calculations and effective theories. We also illustrate the errors induced by using the conventional Luscher approach instead of a more accurate one 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 pi-pi phase shifts from "synthetic" lattice data, providing an optimal strategy and showing which accuracy is needed in these data to obtain the $\rho$ properties with a desired accuracy.