Speaker
Description
Extracting resonance properties from lattice QCD increasingly requires a finite-volume framework capable of treating coupled multi-particle dynamics beyond two-body systems. Here we develop a nonperturbative Hamiltonian framework(NPHF) for general $N$-body finite-volume systems, establishing a direct connection between finite-volume spectra and infinite-volume scattering observables. The framework incorporates lattice and isospin symmetries and provides a unified treatment of coupled channels with different particle numbers in the finite volume. We implement the NPHF in an open-source numerical package and apply it to the $\omega$-meson system, where the $3\pi$ dynamics are treated nonperturbatively and the $\omega$ pole is extracted from the real lattice QCD spectra. Using a controlled four‑particle benchmark built upon the $\sigma-2\pi-4\pi$ model, we validate our framework for few-body finite‑volume problems. This constitutes the first demonstration of finite‑volume calculations incorporating genuine four‑particle sectors. Our work establishes the NPHF as a powerful tool for investigating multi‑hadron resonances and coupled‑channel dynamics from lattice QCD.