Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation

TL;DR

This study uses lattice QCD and the Born-Oppenheimer approximation to investigate the potential existence of a bound state in the $ar bbar du$ system, which could explain the experimental $Z_b(10610)$ resonance.

Contribution

It provides a lattice QCD analysis of the $ar bbar du$ system with static $b$ quarks, revealing a possible bound state near the $Bar B^*$ threshold, linking theory to experimental observations.

Findings

Identified a significant attraction in the $Bar B^*$ channel at small separation.

Extracted an attractive potential $V(r)$ leading to a bound state.

Predicted a bound state close to the $Bar B^*$ threshold, consistent with $Z_b(10610)$.

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 Schr\"odinger 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.