General Hamiltonian Approach to the $\mathbf{N}$-Body Finite-Volume Formalism: Extracting the $\mathbf{\omega}$ Resonance Parameters from Lattice QCD

TL;DR

This paper introduces a nonperturbative Hamiltonian framework that connects lattice QCD finite-volume spectra to scattering observables, enabling precise extraction of resonance parameters like the $ ho$ and $oldsymbol{ extomega}$ mesons.

Contribution

It develops a unified Hamiltonian formalism for N-body systems that accurately relates lattice spectra to physical scattering data, including three-body dynamics.

Findings

Successfully extracted $ ho$ and $ extomega$ resonance parameters from lattice QCD spectra.

Unified treatment of single-, two-, and three-particle dynamics within a single formalism.

Validated the approach using lattice data at different pion masses.

Abstract

We present a nonperturbative Hamiltonian framework (NPHF) to address the general $N$-body problem. This framework rigorously connects finite-volume spectra from lattice QCD to scattering observables from experiment. To demonstrate its applicability, we extract the resonance parameters of the $\omega$ meson by simultaneously analyzing the isoscalar $3\pi$ and isovector $2\pi$ systems. The Hamiltonian unifies single-particle $\omega$, two-particle $\rho\pi$, and three-particle $\pi\pi\pi$ dynamics within a single unitary formalism. Using leading lattice QCD spectra from the Chinese Lattice QCD Collaboration at $m_\pi$ = 208 and 305 MeV, we perform a fit in the isovector and isoscalar channels, accurately describe the lattice spectra and obtain robust determinations of the $\rho$ and $\omega$ pole positions. This work establishes a foundational approach for extracting resonance dynamics from finite-volume spectra. Given the ubiquity of three-body dynamics in exotic hadrons, halo nuclei, and neutron star matter, this general formalism holds broad relevance across particle, nuclear, and astrophysical physics.