Dynamical coupled-channel approaches on a momentum lattice

TL;DR

This paper introduces a novel method for solving coupled-channel scattering equations in discretized momentum space, enabling the study of finite size effects in lattice QCD simulations, with applications to mesons and baryons.

Contribution

It presents a new formalism for analyzing coupled-channel models on a momentum lattice, incorporating boundary conditions relevant for lattice QCD.

Findings

Predicted lattice spectra for sigma(600), f0(980), a0(980), and Lambda(1405).

Demonstrated the method's applicability to S-wave interactions.

Enabled finite size effect analysis in hadronic physics simulations.

Abstract

Dynamical coupled-channel approaches are a widely used tool in hadronic physics that allow to analyze different reactions and partial waves in a consistent way. In such approaches the basic interactions are derived within an effective Lagrangian framework and the resulting pseudo-potentials are then unitarized in a coupled-channel scattering equation. We propose a scheme that allows for a solution of the arising integral equation in discretized momentum space for periodic as well as twisted boundary conditions. This permits to study finite size effects as they appear in lattice QCD simulations. The new formalism, at this stage with a restriction to S-waves, is applied to coupled-channel models for the sigma(600), f0(980), and a0(980) mesons, and also for the Lambda(1405) baryon. Lattice spectra are predicted.