DFG final project report: Lattice QCD investigation of a b-bar b-bar u d tetraquark resonance

Abstract

Quarks typically appear in pairs, known as mesons, or in triplets, known as baryons, with protons and neutrons as well-known representatives of the latter. However, there are also exotic combinations of four quarks, known as tetraquarks, which have gained significant interest, particularly in recent years. This interest arises from the fact that they can be both detected in modern accelerator experiments and increasingly well understood and precisely predicted on a theoretical level with modern numerical calculations. The goal of this project was to study the existence and properties of specific tetraquark systems, consisting of two heavy antiquarks and two light quarks, based on first principles quantum chromodynamics, using numerical lattice field theory calculations. Investigating a $\bar b \bar b u d$ tetraquark resonance with quantum numbers $I(J^P) = 0(1^-)$ proved to be particularly challenging. Within the scope of this project, it was understood through the Born-Oppenheimer approximation that the tetraquark resonance is not located slightly above the lower $B B$ threshold, as previously expected, but considerably higher, above the $B^\ast B^\ast$ threshold. Final results with full lattice QCD calculations beyond the Born-Oppenheimer approximation have yet to be achieved, as this requires the numerical solution of a complex two-channel scattering problem involving a $B B$ and a $B^\ast B^\ast$ channel. However, essential technical steps for such a future computation have been implemented. For the two $\bar b \bar c u d$ tetraquark systems with quantum numbers $I(J^P) = 0(0^+)$ and $I(J^P) = 0(1^+)$, a rigorous finite-volume scattering analysis based on full lattice QCD computations was performed for the first time. This led to the prediction of a weakly bound but stable tetraquark for each of the two systems, as well as a tetraquark resonance approximately $100 \, \text{MeV}$ above the lowest meson-meson threshold ($B D$ or $B^\ast D$, respectively).