Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice

TL;DR

This paper extends L"uscher's formalism to non-zero total momentum frames in lattice QCD, enabling more efficient extraction of scattering phase shifts for resonances like the rho meson.

Contribution

The work generalizes the L"uscher formalism to non-rest frames, allowing broader energy access and improved resonance analysis in lattice simulations.

Findings

Formalism successfully tested with a simple lattice model.

Remarkable agreement between rest-frame and non-rest-frame scattering results.

Method enhances the study of resonances in lattice QCD.

Abstract

Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured from finite periodic lattices. In this work, we generalize the formalism to the case where the total momentum of the particles is non-zero; i.e. the lattice frame is not the center-of-mass frame of the scattering particles. There are several advantages to this procedure including making a wider variety of center of mass energies accessible with a fixed lattice volume, and making the avoided level crossing in a P-wave decay occur with a smaller volume. The formalism is tested with a simple lattice model of two fields with different masses and a 3-point coupling in 3+1 dimensions. We find remarkable agreement between the rest-frame and non-rest-frame scattering.