Zb tetraquark channel and $B{\bar{B}}^{\ast }$ interaction from lattice QCD

Abstract

Two tetraquark candidates $Z_b(10610)$ and $Z_b(10650)$ with flavor structure $\bar{b}b\bar{d}u$ were discovered by Belle experiment in 2011. We present a preliminary $N_f=2$ lattice study of the $\bar{b}b\bar{d}u$ 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 $B{\bar{B}}^{\ast }$: its energy is significantly below $m_B+m_{B\ast }$ for r=[0.1,0.4] fm, which suggests sizable attraction. The attractive potential $V(r)$ between $B$ and ${\bar{B}}^{\ast }$ is extracted assuming that this eigenstate is related exclusively to $B{\bar{B}}^{\ast }$. Assuming a certain form of the potential and solving non-relativistic Schrodinger equation, we find a bound state pole below $B{\bar{B}}^{\ast }$ threshold. For certain parametrizations, the bound state is very close to the $B{\bar{B}}^{\ast }$ threshold - this feature could be related to $Z_b(10610)$ in the experiment.

Comments: 7 pages, 4 figures, Proceedings of Lattice2019, 16-22 June 2019, Wuhan, China; v2 reflects changes in 1912.02656v4 which discusses the same study