Abstract
Two Zb hadrons with exotic quark structure b¯bd¯u were discovered by Belle experiment. We present a lattice QCD study of the b¯bd¯u 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 b¯. The lower eigenstates are related to a bottomonium and a pion. The eigenstate dominated by BB¯⁎ has energy significantly below mB+mB⁎, which points to a sizable attraction for small r. The attractive potential V(r) between B and B¯⁎ is extracted assuming that this eigenstate is related exclusively to BB¯⁎. The Schrödinger equation for BB¯⁎ within the extracted potential leads to one bound state below BB¯⁎ threshold, whose mass depends on the parametrization of the lattice potential. For certain parametrizations, the bound state is very close to the BB¯⁎ threshold and renders a narrow peak in the BB¯⁎ rate above threshold - these features could be related to Zb(10610) in the experiment.
Highlights
Eigen-energies of bbdu system in Fig. 1a indicate that eigenstate dominated by the B B ∗ has significantly lower energy than mB + mB∗ at small separation r between static b and b. This suggests a possible existence of exotic hadrons and related peaks in the cross-section near B B ∗ threshold
We presented a lattice QCD study of a channel with quark structure bbdu, where Belle observed two exotic Zb hadrons
We find significantly attractive potential V (r) between B and B ∗ at small r when the total spin of the heavy quarks is equal to one
Summary
In the present study we consider the Born-Oppenheimer approximation [20], inspired by the study of this system in [18,19] It is applied in molecular physics since ions are much heavier than other degrees of freedom. In the first step we treat b and bas static at fixed distance r (Fig. 1a) and the main purpose is to determine eigen-energies En(r) of this system This energy represents the total energy without the kinetic and rest energies of the b and b , so En(r) is related to the potential V (r) felt by the heavy degrees of freedom. L since the total momenta of light degrees of freedom is not conserved in the presence of static quarks, i.e. pion momentum can change when it scatters on an infinitely heavy Υ.
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