PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Hadron Spectroscopy and Interactions
Two- and three-particle scattering in the (1+1)-dimensional O(3) non-linear sigma model
J. Baeza-Ballesteros* and M.T. Hansen
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Pre-published on: January 23, 2023
Published on: April 06, 2023
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.
DOI: https://doi.org/10.22323/1.430.0050
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