Two Particle States and the $S$-matrix Elements 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 in all three directions. 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.

18 pages, no figures. minor changes compared with previous version

References in corpus (8)

• Two Particle States in an Asymmetric Box and the Elastic Scattering Phases
• A study of pentaquarks on the lattice with overlap fermions
• Calculating the I=2 Pion Scattering Length Using Tadpole Improved Clover Wilson Action on Coarse Anisotropic Lattices
• I=2 Pion Scattering Phase Shift with Wilson Fermions
• Two Particle States in an Asymmetric Box
• I=2 Pion Scattering Length with the Wilson Fermion
• I=2 pion scattering length with the parametrized fixed point action
• I=2 pion-pion scattering phase shift in the continuum limit calculated with two-flavor full QCD

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