Tetraquark channels with $\bar{b}b$ pair in the static limit

Abstract

Belle experiment discovered two hadrons with exotic quark content $Z_b^{+}\simeq \bar{b}b\bar{d}u$. We present a lattice study of the $\bar{b}b\bar{d}u$ systems with various quantum numbers using static bottom quarks. Only one set of quantum numbers that couples to $Z_b$ and ${\rm Y}\pi$ was explored on the lattice before: these studies found an attractive potential between $B$ and ${\bar{B}}^{\ast }$ which leads to a bound state below the threshold. In the present study, we consider the other three sets of quantum numbers. Eigen-energies of the $\bar{b}b\bar{d}u$ system are extracted as a function of separation between $b$ and $\bar{b}$. The resulting eigen-energies do not show any sizable deviation from non-interacting energies of the systems $\bar{b}b+\bar{d}u$ and $\bar{b}u+\bar{d}b$, so no significant attraction or repulsion is found. A slight exception is a small attraction between $B$ and ${\bar{B}}^{\ast }$ at small distance for the quantum number that couples to $Z_b$ and ${\eta }_b\rho$.

Comments: 9 pages, conference: The 38th International Symposium on Lattice Field Theory, LATTICE2021. arXiv admin note: substantial text overlap with arXiv:2109.08560