Doubly Bottom and Bottom-Strange Tetraquarks in the Isoscalar Channel

Abstract

We present our recent investigation on doubly bottom and bottom-strange tetraquarks in the isoscalar channel in search of a possible tetraquark bound state. The calculations are performed on four ensembles with dynamical quark fields up to the charm quark generated by the MILC Collaboration with various lattice spacings. Two volumes have been used to account for finite volume effects. Overlap action has been employed to calculate light and strange quark propagators and NRQCD formulation is utilized for heavy bottom quarks. Finite volume energy has been calculated using the variational method followed by rigorous scattering amplitude analysis à la Lüscher. We find strong evidence for a deeply bound state in the doubly bottom tetraquark channel, but no conclusive evidence for the existence of a bottom-strange tetraquark.

Figures (4)

• Figure 1: Ground-state energy spectra of the $T_{bs}$ system are shown in the top two panels. The bottom panel shows the ground and excited state energy spectrum of the $T_{bb}$ tetraquark. The excited state of $T_{bb}$ is indicated by faded markers. All energies are expressed in units of the corresponding two-meson decay thresholds, and the horizontal axis denotes the spatial lattice extent.
• Figure 2: Upper left: Energy dependence of $p\cot\delta$ normalized to the threshold for $M_{ps}\sim 0.5$ GeV. Upper right: Lattice spacing dependence of $p\cot\delta$ in terms of the threshold for $M_{ps}\sim 0.5$ GeV. Lower: Chiral extrapolation of amplitudes calculated in the continuum limit. The star symbol at the physical pion mass represents the amplitude at the physical point $(a_0^{\text{phys}}E_{BB^*})^{-1}$.
• Figure 3: Continuum-extrapolated results for the axialvector (left) and scalar (right) $bs\bar{u}\bar{d}$ tetraquarks, presented in units of their respective decay thresholds $B^*K$ and $BK$. The colored bands indicate $1\sigma$ uncertainties.
• Figure 4: Mass dependence of the $bb\bar{u}\bar{d}$ tetraquark binding as one bottom quark is replaced by a charm quark and subsequently by a strange quark. The binding energy decreases in magnitude as one of the heavy quark mass is replaced with light quark, becoming weakly bound in the strange sector.