Abstract Two Z b hadrons with exotic quark structure b ¯ b d ¯ u were discovered by Belle experiment. We present a lattice QCD study of the b ¯ b d ¯ 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 B 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 B ¯ ⁎ is extracted assuming that this eigenstate is related exclusively to B B ¯ ⁎ . The Schrodinger equation for B B ¯ ⁎ 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 B B ¯ ⁎ threshold and a narrow peak in the B B ¯ ⁎ rate above threshold - these features could be related to Z b ( 10610 ) in the experiment. We surprisingly find also a deep bound state within the undertaken approximations.

中文翻译：

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来自晶格 QCD 和 Born-Oppenheimer 近似的 Z 四夸克通道

摘要 贝尔实验发现了两个具有奇异夸克结构 b ¯ bd u 的 Z b 强子。我们在静态 b 夸克的近似中提出了 b ¯ bd u 系统的晶格 QCD 研究，其中重夸克的总自旋固定为 1。本征态的能量被确定为 b 和 b 之间的间距 r 的函数。较低的本征态与底鎓和π介子有关。由 BB ¯ ⁎ 支配的本征态的能量明显低于 m B + m B ⁎ ，这表明对小 r 具有相当大的吸引力。B 和 B ¯ ⁎ 之间的吸引势 V ( r ) 被提取，假设该本征态仅与 BB ¯ ⁎ 相关。BB ¯ ⁎ 在提取势内的薛定谔方程导致虚拟束缚态，其质量取决于晶格势的参数化。对于某些参数化，我们发现略低于 BB ¯ ⁎ 阈值的虚拟束缚状态和高于阈值的 BB ¯ ⁎ 率的窄峰——这些特征可能与实验中的 Z b (10610) 有关。我们出人意料地在所进行的近似中也发现了一个深束缚态。