Speaker: Maxwell Hansen (CERN)
Title: Towards three-particle scattering amplitudes from lattice QCD
Abstract: Numerical lattice QCD (LQCD) calculations are necessarily restricted to a finite volume and to Euclidean-signature correlation functions. These limitations complicate the extraction of multi-hadron observables, including scattering amplitudes and transition rates. In particular, it is not possible to directly project out multi-particle in and out states, since the usual LSZ prescription requires Minkowski-signature momenta to take the on-shell limit. Over 30 years ago, Martin Lüscher gave a method to overcome this limitation by thinking of the finite-volume as a tool rather than an unwanted artifact. He derived a quantization condition relating the finite-volume spectrum (available in a lattice calculation) to the physical, infinite-volume 2-to-2 scattering amplitudes. This has since been applied in a large body of numerical calculations to extract hadronic scattering and resonance properties from LQCD. In this seminar, I will discuss recent progress in extending this approach to extract 2-to-3 and 3-to-3 scattering amplitudes. I will review the two-and-three-particle quantization condition that we have derived and describe how it reproduces known results in the limits of weak and strong interactions. I will then discuss recent numerical explorations in which we input infinite-volume observables and predict the corresponding finite-volume three-particle energies.