Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation

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 a virtual bound state, whose mass depends on the parametrization of the lattice potential. For certain parametrizations, we find a virtual bound state slightly below BB¯⁎ threshold and a narrow peak in the BB¯⁎ rate above threshold - these features could be related to Zb(10610) in the experiment. We surprisingly find also a deep bound state within the undertaken approximations.