Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation

Abstract

Two $Z_b$ hadrons with exotic quark structure $\bar bb\bar du$ were discovered by Belle experiment. We present a lattice QCD study of the $\bar bb\bar du$ system in the approximation of static $b$ quarks, where the total spin of heavy quarks is fixed to one. The energies of eigenstates are determined as a function of the separation $r$ between $b$ and $\bar b$. The lower eigenstates are related to a bottomonium and a pion. The eigenstate dominated by $B\bar B^*$ has energy significantly below $m_B+m_{B^*}$, which points to a sizable attraction for small $r$. The attractive potential $V(r)$ between $B$ and $\bar B^*$ is extracted assuming that this eigenstate is related exclusively to $B\bar B^*$. The Schrödinger equation for $B\bar B^*$ within the extracted potential leads to one bound state below $B\bar B^*$ threshold, whose mass depends on the parametrization of the lattice potential. For certain parametrizations, the bound state is very close to the $B\bar B^*$ threshold and renders a narrow peak in the $B\bar B^*$ rate above threshold - these features could be related to $Z_b(10610)$ in the experiment.