Generalized boost transformations in finite volumes and application to Hamiltonian methods

TL;DR

This paper introduces a new method to generalize boost transformations in finite-volume Hamiltonian systems, improving the analysis of hadron interactions in lattice QCD by enabling energy-independent calculations at finite boosts.

Contribution

The paper presents a novel approach to extend boost transformations to finite-volume Hamiltonians, overcoming limitations of existing energy-dependent methods in lattice QCD analyses.

Findings

Numerical comparisons demonstrate the effectiveness of the new boost prescription.

Application to a phenomenological ππ scattering example validates the approach.

Method facilitates energy-independent Hamiltonian formulations in moving frames.

Abstract

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian.In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological $\pi\pi$ scattering example.