Few-body physics

TL;DR

This paper reviews the theoretical challenges and recent methodological advances in using Lattice QCD to study few-body systems, including scattering, resonances, and decay processes relevant for particle and nuclear physics.

Contribution

It discusses formal challenges and recent generalizations of Lattice QCD frameworks for analyzing few-body observables, including scattering amplitudes and form factors.

Findings

Review of formal challenges in Lattice QCD for few-body systems

Description of Luscher and Lellouch-Luscher formalisms and their generalizations

Identification of outstanding problems in the field

Abstract

Few-body hadronic observables play an essential role in a wide number of processes relevant for both particle and nuclear physics. In order for Lattice QCD to offer insight into the interpretation of few-body states, a theoretical infrastructure must be developed to map Euclidean-time correlation functions to the desired Minkowski-time few-body observables. In this talk, I review the formal challenges associated with the studies of such systems via Lattice QCD, as first introduced by Maiani and Testa, and I also review the methodology to circumvent said limitations. The first main example of the latter is the formalism by Luscher to analyze elastic scattering and a second is the method by Lellouch and Luscher to analyze weak decays. I discus recent theoretical generalizations of these frameworks that allow for the determination of scattering amplitudes, resonances, nonlocal contribution to matrix elements, and form factors below and above inelastic thresholds. Finally, I outline outstanding problems, including those that are now beginning to be addressed.