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

Abstract

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 Lüscher's formula which establishes a similar relation in elastic scattering.

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

References in corpus (1)

• I=2 $\pi \pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved Dynamical Quarks

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