Search for $\bar{b} \bar{b} u s$ and $\bar{b} \bar{c} u d$ tetraquark bound states using lattice QCD

Abstract: We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\bar b \bar b u s$ system with quantum numbers $J^P = 1^+$ as well as the $\bar b \bar c u d$ systems with quantum numbers $I(J^P) = 0(0^+)$ and $I(J^P) = 0(1^+)$. We carry out computations on five gauge-link ensembles with $2 + 1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable $\bar b \bar b u s$ tetraquark with binding energy $(-86 \pm 22 \pm 10) \, \text{MeV}$ and mass $(10609 \pm 22 \pm 10) \, \text{MeV}$. For the $\bar b \bar c u d$ systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.