Shallow $T_{bc}$ states from an EFT analysis of $B^{(\ast )}{\bar{D}}^{(\ast )}$ scattering on the lattice

Abstract

We present an effective field theory (EFT) framework for coupled-channel $B^{(\ast )}{\bar{D}}^{(\ast )}$ scattering, applying it to recent lattice QCD results by Alexandrou et al. [Phys. Rev. Lett. 132, 151902 (2024)]. Two complementary EFT approaches are developed: (1) A low-energy theory near the $B\bar{D}$ ($J=0$) and $B^{\ast }\bar{D}$ ($J=1$) thresholds, where coupled-channel effects are integrated out; (2) A 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 $B{\bar{D}}^{\ast }$ and $B^{\ast }{\bar{D}}^{\ast }$ 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.

Comments: 15 pages, 8 figures