Coupled-channel scattering in 1+1 dimensional lattice model

TL;DR

This paper derives a generalized Lüscher's formula for coupled-channel scattering in 1+1 dimensions, applies it to a lattice model, and uses Monte Carlo simulations to extract scattering amplitudes from finite-volume spectra.

Contribution

It introduces a new generalized Lüscher's formula for coupled-channel scattering in 1+1 dimensions and demonstrates its application through lattice simulations.

Findings

Successfully derived the generalized Lüscher's formula.

Validated the formula with Monte Carlo simulations.

Extracted scattering amplitudes from finite-volume spectra.

Abstract

Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering lattice model is presented, the model represents a two-coupled-channel resonant scattering scalars system. The Monte Carlo simulation is performed on finite lattices and in various moving frames. The 2D generalized L\"uscher's formula is used to extract the scattering amplitudes for the coupled-channel system from the discrete finite-volume spectrum.