Shallow T b c states from an EFT analysis of B ( * ) D ¯ ( * ) scattering on the lattice

We present an effective field theory (EFT) framework for coupled-channel B ( * ) D ¯ ( * ) scattering, applying it to recent lattice QCD results by Alexandrou []. Two complementary EFT approaches are developed: (1) a low-energy theory near the B D ¯ ( J = 0 ) and B * D ¯ ( J = 1 ) thresholds, where coupled-channel effects are integrated out; (2) coupled-channel formulation, where all relevant momentum scales are treated as soft, incorporating contact interactions and one-pion exchange (OPE). Importantly, OPE contributes to the lowest channels only through off-diagonal transitions, thus resulting in the appearance of the left-hand cut from two-pion exchange. The two approaches yield mutually consistent results, supporting the existence of shallow bound states in both channels, in agreement with the lattice findings. The finite-volume spectra and extracted pole positions show a near-degeneracy in J = 0 and J = 1 channels, consistent with heavy-quark spin symmetry (HQSS). Using HQSS, we predict additional shallow bound states near the B D ¯ * and B * D ¯ * thresholds, which are accessible to future lattice simulations. The effect of OPE on the finite volume spectra is found to be small, with only moderate impact on HQSS partners.