Extracting scattering amplitudes for arbitrary two-particle systems with one-particle left-hand cuts via lattice QCD

TL;DR

This paper develops a comprehensive formalism to extract physical scattering amplitudes from finite-volume lattice QCD spectra, accounting for complex left-hand cuts and multi-channel effects, enhancing the analysis of two-particle systems.

Contribution

It introduces a general, exact method relating finite-volume spectra to physical scattering amplitudes for arbitrary two-particle systems with complex interactions.

Findings

Derives a relation between finite-volume spectrum and infinite-volume scattering amplitudes.

Incorporates effects of left-hand branch cuts due to single-particle exchanges.

Applicable to multi-channel, non-identical, and spinning particles.

Abstract

We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method first relates the finite-volume spectrum to an infinite-volume short-range quantity, denoted \mathcal{M}_0, and then relates the latter to the physical scattering amplitudes via known integral equations. The derivation of both relations is performed using all-orders perturbation theory and is exact up to neglected exponentially suppressed volume dependence. The relations hold for arbitrary two-particle systems with any number of coupled channels, non-identical and non-degenerate particles, and any intrinsic spin.