$Z_b$ tetraquark channel and $B\bar B^*$ interaction

Abstract

Two tetraquark candidates $Z_b(10610)$ and $Z_b(10650)$ with flavor structure $\bar bb\bar du$ were discovered by Belle experiment in 2011. We present a preliminary $N_f=2$ lattice 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 ground and the excited eigen-energies are determined as a function of separation $r$ between $b$ and $\bar b$. The lower eigenstates are related to a bottomonium and a pion. One of the higher eigenstates is dominated by $B\bar B^*$: its energy is significantly below $m_B+m_{B*}$ for r=[0.1,0.4] fm, which suggests sizable attraction. The attractive potential $V(r)$ between $B$ and $\bar B^*$ is extracted assuming that this eigenstate is related exclusively to $B\bar B^*$. Assuming a certain form of the potential at small $r<0.1~$fm and solving non-relativistic Schrodinger equation, we find a virtual bound state pole $32^{-29}_{+5}~$MeV below $B\bar B^*$ threshold. This pole leads to a narrow peak in the cross-section just above threshold that could be perhaps related to experimental $Z_b$ resonances. Given all these approximations, we surprisingly find also a deep bound state $403\pm 70~$MeV below $B\bar B^*$ threshold. If such a $Z_b$ state exists, it could be experimentally searched in the accurate dependence of rates on $\Upsilon(1S)\pi^+$ invariant mass.