Hamiltonian effective field theory in elongated or moving finite volume

TL;DR

This paper extends Hamiltonian effective field theory to elongated and moving finite volumes, enabling better analysis of lattice QCD spectra and partial-wave scattering information, especially when combining elongation and motion.

Contribution

It introduces a formalism for partial-wave mixing in elongated and moving finite volumes within Hamiltonian effective field theory, applicable to lattice QCD analyses.

Findings

Improved scattering phase shift extraction from lattice QCD data.

Enhanced uncertainty reduction when combining elongated and moving frames.

Validated method with isospin-2 ππ scattering results.

Abstract

We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively. We also consider the combination of the two systems when directions of the elongation and the moving momentum are aligned. This extension should also be applicable in any Hamiltonian formalism. As a demonstration, we analyze lattice QCD results for the spectrum of an isospin-2 $\pi\pi$ scattering system and determine the $s$, $d$, and $g$ partial-wave scattering information. The inclusion of lattice simulation results from moving frames significantly improves the uncertainty in the scattering information.