Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels

A novel effective-field-theory-based approach is implemented for extracting two-body scattering information from finite volume energies, serving as an alternative to L\"uscher's method. By explicitly incorporating one-pion exchange, the approach quantitatively accounts for effects related to left-hand cuts and range corrections from the longest-range interactions. The method utilizes the plane wave basis instead of the conventional partial wave expansion, thereby also naturally including partial wave mixing effects resulting from rotational symmetry breaking in a cubic box. Applied to the lattice data for $DD^*$ scattering at a pion mass of 280 MeV, it reveals the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the $T_{cc}(3875)^+$ state, extracted from the finite-volume energy levels while taking into account left-hand cut effects, range corrections, and partial-wave mixing, appears to be consistent with a near-threshold resonance.