Resonances in Coupled-Channel Scattering

TL;DR

This paper discusses how lattice QCD and finite volume formalism are used to analyze coupled-channel scattering amplitudes, enabling the extraction of resonance properties of excited hadrons from finite volume spectra.

Contribution

It demonstrates the application of advanced lattice QCD techniques and formalism to reliably determine coupled-channel scattering amplitudes and resonance parameters.

Findings

Finite volume spectra can be used to extract scattering amplitudes.

Resonance poles and couplings are obtained by analytic continuation.

Multiple channels and quantum numbers are analyzed successfully.

Abstract

Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\pi$, $K$ and $\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain coupled-channel scattering amplitudes from lattice QCD. Using large diverse bases of operators it is possible to obtain reliable finite volume spectra at energies where multiple channels are open. Utilising the finite volume formalism proposed by L\"uscher and extended by several others, scattering amplitudes can be extracted from the finite volume spectra. Recent applications will be discussed where the energy dependence of scattering amplitudes is mapped out in several quantum numbers. These are then continued to complex energies to extract resonance poles and couplings.