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

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 QC]) 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 pi K 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 a 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)articular the required high precision on the lattice data, the sigma(600), the P-wave resonances K*(892) and rho(770), and the repulsive pi K, pi pi phases are analyzed as well.