Two- and three-particle scattering in the (1+1)-dimensional O(3) non-linear sigma model

TL;DR

This paper investigates two- and three-particle scattering in the (1+1)-dimensional O(3) non-linear sigma model using numerical simulations, comparing results with exact predictions and exploring finite-volume effects.

Contribution

It introduces a numerical approach for studying multi-particle scattering in the O(3) model and compares lattice results with analytic predictions, extending to three-particle sectors.

Findings

Lattice results agree with exact two-particle scattering predictions.

Finite-volume energies can be reliably extrapolated to the continuum.

Ongoing work on three-particle scattering formalism comparison.

Abstract

We study two- and three-particle scattering in the O(3) non-linear sigma model in 1+1 dimensions, focusing on the isospin-1 and isospin-2 channels for two particles, and the isospin-3 channel for three. We perform numerical simulations for four values of the physical volume, each at three lattice spacings, using a three-cluster generalization of the cluster update algorithm, and directly extrapolate the determined finite-volume energies to the continuum at fixed physical volume. Lattice results for two particles are then compared against exact predictions, obtained by combining analytic results for the scattering phase shifts and the (1+1)-dimensional two-particle formalism that relates these to finite-volume energies. Analogous comparisons in the three-particle sector are underway, making use of the three-particle relativistic-field-theory finite-volume formalism.