The Lüscher scattering formalism on the $t$-channel cut

Abstract

The Lüscher scattering formalism, the standard approach for relating the discrete finite-volume energy spectrum to two-to-two scattering amplitudes, fails when analytically continued so far below the infinite-volume two-particle threshold that one encounters the $t$-channel cut. This is relevant, especially in baryon-baryon scattering applications, as finite-volume energies can be observed in this below-threshold regime, and it is not clear how to make use of them. In this talk, we present a generalization of the scattering formalism that resolves this issue, allowing one to also constrain scattering amplitudes on the $t$-channel cut.

Comments: 11 pages, 4 figures, talk given at "The 39th International Symposium on Lattice Field Theory", 08th-13th August 2022, Bonn, Germany, v2: shortened to match published version