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. Key words: S-matrix elements, lattice QCD, finite size effects. PACS: 12.38.Gc, 11.15.Ha 1