# Scattering processes and resonances from lattice QCD

## TL;DR

This paper reviews how lattice QCD techniques are used to study hadron resonances, providing insights into their properties and the underlying strong interaction dynamics in a non-perturbative regime.

## Contribution

It presents the leading lattice QCD approach for extracting scattering amplitudes and resonance properties from finite-volume spectra, highlighting recent progress and challenges.

## Key findings

- Lattice QCD can determine resonance masses and widths.
- Finite-volume spectra encode scattering information.
- Progress addresses current methodological challenges.

## Abstract

The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.