Finite volume effects in pion-kaon scattering and reconstruction of the kappa(800) resonance

TL;DR

This paper investigates finite-volume effects in lattice QCD simulations of the broad kappa(800) resonance using unitarized chiral perturbation theory, providing methods to extract the resonance signal from lattice spectra.

Contribution

It introduces a framework for analyzing finite-volume effects in pion-kaon scattering and predicts lattice levels for various meson resonances, aiding in the extraction of the kappa(800).

Findings

Predicted lattice levels for piK scattering and other resonances.

Estimated the lattice data precision needed for clear resonance extraction.

Analyzed effects for multiple meson resonances and phases.

Abstract

Simulating the kappa(800) on the lattice is a challenging task that starts to become feasible due to the rapid progress in recent-years lattice QCD calculations. As the resonance is broad, special attention to finite-volume effects has to be paid, because no sharp resonance signal as from avoided level crossing can be expected. In the present article, we investigate the finite volume effects in the framework of unitarized chiral perturbation theory using next-to-leading order terms. After a fit to meson-meson partial wave data, lattice levels for piK scattering are predicted. In addition, levels are shown for the quantum numbers in which the sigma(600), f_0(980), a_0(980), phi(1020), K*(892), and rho(770) appear, as well as the repulsive channels. Methods to extract the kappa(800) signal from the lattice spectrum are presented. Using pseudo-data, we estimate the precision that lattice data should have to allow for a clear-cut extraction of this resonance. To put the results into context, in particular the required high precision on the lattice data, the sigma(600), the P-wave resonances K*(892) and rho(770), and the repulsive piK, pipi phases are analyzed as well.