Role of left-hand cut contributions on pole extractions from lattice data: Case study for $T_{cc}(3875)^+$

Résumé : We discuss recent lattice data for the $T_{cc}(3875)^+$ state to stress a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the $DD^*$ system for the pion mass exceeding its physical value, the effective-range expansion is valid only in the very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes.