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

Abstract

Simulating the κ(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 πK scattering are predicted. In addition, levels are shown for the quantum numbers in which the σ(600), f 0 (980), a 0 (980), φ(1020), K * (892), and ρ(770) appear, as well as the repulsive channels. Methods to extract the κ(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 σ(600), the Pwave resonances K * (892) and ρ(770), and the repulsive πK, ππ phases are analyzed as well.

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

“…This does not, however, change the underlying idea of our proposal -considering a given effective field theory (relativistic or non-relativistic) in a finite volume, calculating the spectrum numerically and fitting the low-energy constants to the spectrum. Note also that a very similar strategy is pursued within the framework of the unitary ChPT in a finite volume [13][14][15][16][17], which is used in the analysis of data in the two-particle sector. A possible alternative scheme in the three-body sector based on the isobar approximation was recently discussed in ref.…”

“…The approach remains conceptually the same for coupled-channel inelastic scattering [2][3][4][5][6][7][8][9] and has already been used to analyze the data in the two-channel system [10][11][12]. A related approach that boils down to using a different parameterization of the infinite-volume amplitudes goes under the name of "unitary ChPT in a finite volume" [13][14][15][16][17] and has already been used in ref. [18] to analyze P -wave ππ scattering and to study the properties of the ρ-meson.…”

The optical potential on the lattice

“…In case when only two-particle coupled channels appear, one can make use of the coupled-channel Lüscher equation [2][3][4][5][6][7][8][9] and fit a simple pole parameterization for the multi-channel K-matrix elements to the measured energy spectrum in the finite volume [10][11][12]. A more sophisticated parameterization of the K-matrix elements, which is applicable in a wider range of the energies, can be obtained using unitarized chiral perturbation theory (ChPT) [13][14][15][16][17]. In the one-channel case such an approach has been successfully applied, e.g., in ref.…”

Matrix elements of unstable states

“…[17,18]). Recently, a generalization of Lüscher's approach in the presence of 3-particle intermediate states has been proposed [19].…”