The coupled-channel scattering on a torus
Peng Guo, Jozef Dudek, Robert Edwards, Adam P. Szczepaniak
TL;DR
This paper derives a generalized Lüscher's formula for coupled-channel scattering in finite volume, facilitating the extraction of scattering amplitudes from lattice QCD data, with potential applications in hadron physics.
Contribution
It introduces a new formalism based on the Hamiltonian approach for coupled-channel scattering in moving frames, extending existing methods to more complex systems.
Findings
Derived a generalized Lüscher's formula for coupled channels
Discussed strategies for extracting scattering amplitudes from finite-volume spectra
Illustrated methods with a toy model of two-channel resonant scattering
Abstract
Based on the Hamiltonian formalism approach, a generalized L\"uscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some strategies for extracting scattering amplitudes for a coupled-channel system from the discrete finite-volume spectrum are discussed and illustrated with a toy model of two-channel resonant scattering. This formalism will, in the near future, be used to extract information about hadron scattering from lattice QCD computations.
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