Unstable particles in finite volume: The broken phase of the $4$-d $O(4)$ non-linear $σ$-model

Frank Zimmermann; Jörg Westphalen; Meinulf Göckeler; Hans A. Kastrup

doi:10.1016/0920-5632(93)90347-9

paper

Unstable particles in finite volume: The broken phase of the $4$ -d $O (4)$ non-linear $σ$ -model

arXiv:hep-lat/9211029 · doi:10.1016/0920-5632(93)90347-9

Abstract

According to a proposal of Lüscher 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 4-dimensional $O (4)$ non-linear $σ$ -model in a Monte-Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the $\sg$-particle in our case. We observe the $\sg$-resonance and extract its mass and its width.

4 pages LaTeX, 4 PS figures, LATTICE'92 contribution

Unstable particles in finite volume: The broken phase of the 4-d O(4) non-linear σ-model

Abstract

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Unstable particles in finite volume: The broken phase of the $4$ -d $O (4)$ non-linear $σ$ -model