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

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

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

Scientific paper

10.1016/0920-5632(93)90347-9

According to a proposal of L\"uscher 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 $\sigma$-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.

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