Higher order quantization conditions for two-body scattering with spin
Lucas Chandler (Physics Department, The George Washington University, Washington, DC 20052, USA)
; Frank X. Lee (Physics Department, The George Washington University, Washington, DC 20052, USA); Andrei Alexandru (Physics Department, The George Washington University, Washington, DC 20052, USA)
We examine the Lüscher quantization condition to high order for the scattering of a spinless particle and a spin- particle in a periodic box. First, we derive the quantization conditions in a nonrelativistic framework up to total angular momentum in both cubic and elongated geometries, and for both rest and moving frames. Then, we introduce a method to transparently cross-check their convergence, using both quantized energy levels in the box and infinite-volume phase shifts for the same potential. We clarify how to incorporate spin-orbit coupling into the formalism and show in detail how the quantization conditions converge order by order in the various irreducible representations. In all, we validated 19 quantization conditions (12 in cubic box, 7 in elongated box). This is a necessary step in applying the method in precision studies of systems in finite volume with half-integer spin, such as meson-baryon scattering.
