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We discuss recent lattice data for the $T_{cc}(3875)^+$ state to stress, forthe first time, a potentially strong impact of left-hand cuts from the one-pionexchange on the pole extraction for near-threshold exotic states. Inparticular, if the left-hand cut is located close to the two-particlethreshold, which happens naturally in the $DD^*$ system for the pion massexceeding its physical value, the effective-range expansion is valid only in avery limited energy range up to the cut and as such is of little use toreliably extract the poles. Then, an accurate extraction of the pole locationsrequires the one-pion exchange to be implemented explicitly into the scatteringamplitudes. Our findings are general and potentially relevant for a wide classof hadronic near-threshold states.

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