Finite-volume Hamiltonian method for $\pi\pi$ scattering in lattice QCD

TL;DR

This paper presents a finite-volume Hamiltonian approach to extract $\pi\pi$ scattering observables from lattice QCD spectra, applicable to multiple channels and frames, enabling direct determination of hadron properties.

Contribution

It introduces a Hamiltonian framework for fitting lattice spectra to determine scattering parameters and hadron properties in a multi-channel, multi-frame setting.

Findings

Effective extraction of scattering observables from lattice spectra.

Application to both S- and P-wave channels.

Extension to multi-channel scattering cases.

Abstract

Within a formulation of $\pi\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolving scattering observables from lattice QCD spectra. We consider spectra in the centre-of-mass and moving frames for both S- and P-wave cases. Furthermore, we investigate the multi-channel case. Here we study the use of the Hamiltonian framework as a parametrization that can be fit directly to lattice spectra. Through this method, the hadron properties, such as mass, width and coupling, can be directly extracted from the lattice spectra.