Two Pathways for Accessing Amplitudes with Left-Hand Cuts in Finite Volumes
Accessing scattering amplitudes with lattice QCD has become a vital tool in our theoretical understanding of the excited hadron spectrum. A key component is the non-perturbative formalism which relates finite-volume lattice QCD spectra to infinite-volume reaction amplitudes, known as the Lüscher formalism. However, the standard framework is not valid for energies below threshold where cross-channel exchanges can produce left-hand cuts. Members of ExoHad have recently released two works which present pathways to access amplitudes with nearby left-hand cuts, which have been observed to affect physics in interesting systems such as the $T_{cc}$ in $DD^*$ scattering. Andrew Jackura (W&M) and Raúl Briceño (UCB, co-PI) and their collaborators have extended the Lüscher framework to accommodate single-particle exchange effects, which has recently been accepted into JHEP. This work provides a complete framework to resolve left-hand-cut physics in finite-volume studies, in particular for future lattice QCD applications. Andrew Jackura, as well as Adam Szczepaniak (IU & JLab, co-PI) and Sebastian Dawid (UW) have also published a novel approach to accessing two-particle scattering amplitudes with left-hand-cuts from finite-volume lattice QCD calculations, published on Phys. Lett. B. In this work, the formalism is derived using the analytic structure of partial wave amplitudes to construct a finite-volume quantization condition which is free from left-hand-cut singularities, alleviating a restriction on the usual Lüscher quantization condition. This new approach may shed light onto the analytic properties of finite-volume amplitudes. Both of these new analysis frameworks are currently being investigated for numerical applications and consistency by members of ExoHad.