Phase shift formulas for baryon-baryon scattering in elongated boxes

TL;DR

This paper derives formulas relating baryon-baryon scattering phase shifts to energy spectra in elongated and asymmetric lattice volumes, aiding phase shift extraction from lattice QCD data.

Contribution

It extends the phase shift formulas to elongated boxes, twisted boundary conditions, and moving frames, enhancing lattice QCD analysis capabilities.

Findings

Derived relations for phase shifts in elongated boxes.

Extended framework to twisted boundary conditions.

Applicable to moving frame lattice calculations.

Abstract

We have established the relations between the baryon-baryon scattering phase shifts and the two-particle energy spectrum in the elongated box. We have studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. This will be helpful to extract the phase shifts in the continuum from lattice QCD data using asymmetric volumes.