Scattering phases on finite lattices in the broken phase of the four-dimensional O(4)-\phi^4 theory

TL;DR

This paper demonstrates how to determine scattering phases and resonance properties in the broken phase of the 4D O(4) model using finite lattice simulations, confirming results with perturbative calculations.

Contribution

It applies Luescher's method to the broken phase of the 4D O(4) model, enabling non-perturbative study of scattering and unstable particles on finite lattices.

Findings

Successfully extracted sigma-resonance mass and width.

Results agree with perturbative calculations.

Demonstrated applicability of Luescher's method in this context.

Abstract

According to a proposal of Luescher it is possible to determine elastic scattering phases in infinite volume from the energy spectrum of two-particle states in a periodic box. We demonstrate the applicability of this method in the broken phase of the four-dimensional O(4) non-linear sigma-model in a Monte Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the sigma-particle in our case. We observe the sigma-resonance and extract its mass and width. In all scattering channels investigated the results are completely consistent with perturbative calculations.