Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

Abstract

Abstract. We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.

Resonance Extraction from the Finite Volume

“…(1) and the Lüscher formalism can be found, e.g., in Ref. [5]. The integration over momenta in the two-body propagator G is reduced to a sum due to the periodic boundary conditions in the finite volume, G →G.…”

“…[5] for the f 0 (980). This case is particularly interesting because the resonance is situated close to the S-wave KK threshold.…”

“…Indeed, in Ref. [5] it was shown that by removing the f 0 (980) the amplitude changes drastically but the level spectrum in the finite volume shows only rather small changes and the qualitative L-dependence of the levels stays the same. In Refs.…”

“…In Refs. [4,5] it was proposed to modify the boundary conditions for the strange quark to remove the influence of the threshold. In the notation used here, this results in a modifiedG.…”

“…In the volume-dependent spectrum of eigenvalues, "avoided level crossing" is usually taken as a signal of a resonance, but this criterion has been shown insufficient for resonances with larger widths [1][2][3][4][5]. For resonances with a single, two-body decay channel, one often uses Lüscher's approach to extract phase shifts from the discrete energy levels in the box [6,7].…”