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

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 $\ddot{I}‰$ meson by simultaneously analyzing the isoscalar $3\ddot{I}€$ and isovector $2\ddot{I}€$ systems. The Hamiltonian unifies single-particle $\ddot{I}‰$, two-particle $\ddot{I}\ddot{I}€$, and three-particle $\ddot{I}€\ddot{I}€\ddot{I}€$ dynamics within a single unitary formalism. Using leading lattice QCD spectra from the Chinese Lattice QCD Collaboration at $m_{\ddot{I}}€$ = 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 $\ddot{I}$ and $\ddot{I}‰$ 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.

10 pages, 2 figures