An extension to the Luscher's finite volume method above inelastic threashold (formalism)

Understand

An extension of the Luscher's finite volume method above inelastic thresholds is proposed.

• It is fulfilled by extendind the procedure recently proposed by HAL-QCD Collaboration for a single channel system.
• Focusing on the asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave functions (equal-time) near spatial infinity, a coupled channel extension of effective Schrodinger equation is constructed by introducing an energy-independent interaction kernel.
• Because the NBS wave functions contain the information of T-matrix at long distance, S-matrix can be obtained by solving the coupled channel effective Schrodinger equation in the infinite volume.