Bound Isoscalar Axial-Vector bcu¯d¯ Tetraquark Tbc from Lattice QCD Using Two-Meson and Diquark-Antidiquark Variational Basis

Abstract

We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content bcu¯d¯, isospin I=0, and axial-vector JP=1+ quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from ∼0.058 to ∼0.12  fm, and at five different values of valence light quark mass mu/d, corresponding to pseudoscalar meson mass Mps of about 0.5, 0.6, 0.7, 1.0, and 3.0 GeV. The energy eigenvalues in the finite volume are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as diquark-antidiquark operators. The continuum limit estimates for DB¯* elastic S-wave scattering amplitude are extracted from the lowest finite-volume eigenenergies, corresponding to the ground states, using amplitude parametrizations supplemented by a lattice spacing dependence. Light quark mass mu/d dependence of the DB¯* scattering length (a0) suggests that at the physical pion mass a0phys=+0.57(−5+4)(17)  fm, which clearly points to an attractive interaction between the D and B¯* mesons that is strong enough to host a real bound state Tbc, with a binding energy of −43(−7+6)(−24+14)  MeV with respect to the DB¯* threshold. We also find that the strength of the binding decreases with increasing mu/d and the system becomes unbound at a critical light quark mass mu/d* corresponding to Mps*=2.73(21)(19)  GeV. Published by the American Physical Society 2024