Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering

Details Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering

2005-08-25

arxiv.org/abs/hep-lat/0508022v2

Int.J.Mod.Phys. A21 (2006) 847-850

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, typeset with ws-ijmpa.cls. Talk presented at International Conference on QCD and Hadronic Physics, June 16-20, 2005,

Scientific paper

10.1142/S0217751X06032150

Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions. A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.

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