Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules,Communications in Theoretical Physics

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Analysis of the tetraquark and hexaquark molecular states with the QCD sum rules
Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2021-04-09 , DOI: 10.1088/1572-9494/abee0d
Zhi-Gang Wang

In this article, we construct the color-singlet-color-singlet type currents and the color-singlet-color-singlet-color-singlet type currents to study the scalar ${D}^{* }{\bar{D}}^{* }$ , ${D}^{* }{D}^{* }$ tetraquark molecular states and the vector ${D}^{* }{D}^{* }{\bar{D}}^{* }$ , ${D}^{* }{D}^{* }{D}^{* }$ hexaquark molecular states with the QCD sum rules in details. In calculations, we choose the pertinent energy scales of the QCD spectral densities with the energy scale formula $\mu =\sqrt{{M}_{T}^{2}-{(2{{\mathbb{M}}}_{c})}^{2}}$ and $\sqrt{{M}_{H}^{2}-{(3{{\mathbb{M}}}_{c})}^{2}}$ for the tetraquark and hexaquark molecular states respectively in a consistent way. We obtain stable QCD sum rules for the scalar ${D}^{* }{\bar{D}}^{* }$ , ${D}^{* }{D}^{* }$ tetraquark molecular states and the vector ${D}^{* }{D}^{* }{\bar{D}}^{* }$ hexaquark molecular state, but cannot obtain stable QCD sum rules for the vector ${D}^{* }{D}^{* }{D}^{* }$ hexaquark molecular state. The connected (nonfactorizable) Feynman diagrams at the tree level (or the lowest order) and their induced diagrams via substituting the quark lines make positive contributions for the scalar ${D}^{* }{D}^{* }$ tetraquark molecular state, but make negative or destructive contributions for the vector ${D}^{* }{D}^{* }{D}^{* }$ hexaquark molecular state. It is of no use or meaningless to distinguish the factorizable and nonfactorizable properties of the Feynman diagrams in the color space in the operator product expansion so as to interpret them in terms of the hadronic observables, we can only obtain information about the short-distance and long-distance contributions.

中文翻译：

使用 QCD 和规则分析四夸克和六夸克分子态

在本文中，我们构造了颜色-单线-颜色-单线型电流和颜色-单线-颜色-单线-颜色-单线型电流来研究标量 ${D}^{* }{\bar{D}}^{* }$ 、 ${D}^{*}{D}^{* }$ 四夸克分子态和矢量 ${D}^{* }{D}^{* }{\bar{D}}^{* }$ 、 ${D}^{* }{D}^{* }{D}^{* }$ 六夸克分子态与 QCD 和详细规则。在计算中，我们以一致的方式分别选择具有能量标度公式 $\mu =\sqrt{{M}_{T}^{2}-{(2{{\mathbb{M}}}_{c})}^{2}}$ 和 $\sqrt{{M}_{H}^{2}-{(3{{\mathbb{M}}}_{c})}^{2}}$ 四夸克和六夸克分子态的 QCD 谱密度的相关能标。我们得到了标量 ${D}^{* }{\bar{D}}^{* }$ 、 ${D}^{*}{D}^{* }$ 四夸克分子态和向量 ${D}^{* }{D}^{* }{\bar{D}}^{* }$ 六夸克分子态的稳定QCD求和规则，但不能得到向量的稳定QCD求和规则 ${D}^{* }{D}^{* }{D}^{* }$ 六夸克分子态。树级（或最低阶）的连通（不可分解）费曼图及其通过代入夸克线的诱导图对标量 ${D}^{*}{D}^{* }$ 四夸克分子态做出正贡献，但对矢量 ${D}^{* }{D}^{* }{D}^{* }$ 六夸克分子态做出负或破坏性贡献。在算子乘积展开中区分颜色空间中费曼图的可分解和不可分解性质以用强子可观测量来解释它们是没有用或没有意义的，我们只能获得关于短距离和不可分解的信息。远距离贡献。

更新日期：2021-04-09

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