Two-particle multichannel systems in a finite volume with arbitrary spin

Abstract

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin, momentum, and masses in a finite volume with either periodic or twisted boundary conditions is presented. Although emphasis is placed in cubic volumes, the result holds for asymmetric volumes. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. For hadronic systems the range of the interaction is set by the inverse of the pion mass, m_pi, and as a result the formalism presented is suitable for m_pi L >> 1. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.

12 pages, 2 figures, minor typos corrected, results remains unchanged, corrected some of the references

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