Finite-volume quantization condition from the $N/D$ representation

TL;DR

This paper introduces a novel, model-independent method based on the $N/D$ representation to extract hadronic resonances from lattice QCD data, extending the applicability of finite-volume quantization conditions.

Contribution

It develops a new formalism that relates finite-volume spectra to the scattering amplitude using the $N/D$ approach, valid even at energies with left-hand cuts.

Findings

Formalism derived from unitarity and analyticity principles.

Quantization condition applicable at energies with left-hand cuts.

Provides a framework for extracting resonances from lattice QCD.

Abstract

We propose a new model-independent method for determining hadronic resonances from lattice QCD. The formalism is derived from the general principles of unitarity and analyticity, as encoded in the $N/D$ representation of a partial-wave two-body amplitude. The associated quantization condition relates the finite-volume spectrum to the infinite-volume numerator, $\mathcal{N}$, used to reconstruct the scattering amplitude from dispersive relations. Unlike the original L\"uscher condition, this new formalism is valid for energies coinciding with the left-hand cuts from arbitrary one- and multi-particle exchanges.