The L\"uscher scattering formalism on the $t$-channel cut

TL;DR

This paper extends the Lüscher scattering formalism to include the $t$-channel cut region, enabling the use of below-threshold finite-volume energies to constrain scattering amplitudes, especially in baryon-baryon interactions.

Contribution

The authors generalize the Lüscher formalism to handle the $t$-channel cut, addressing a key limitation in analyzing below-threshold energies.

Findings

Formalism now constrains scattering amplitudes on the $t$-channel cut.

Applicable to baryon-baryon scattering below threshold.

Enables use of finite-volume energies in previously inaccessible regimes.

Abstract

The L\"uscher 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.