论文标题
Tetraquark分子状态的Landau方程和QCD总和规则
Landau equation and QCD sum rules for the tetraquark molecular states
论文作者
论文摘要
夸克和粘合剂是限制的对象，不能放在大规模上，使用Landau方程来研究QCD总规则中的Feynman图表是值得怀疑的。此外，我们在欧几里得深处进行了运营商的产品扩展，$ p^2 \至 - \ infty $，其中不存在Landau奇点。 Landau方程服务器是动量空间中的运动学方程式，并且独立于彩色空间中Feynman图的可分化和不可分割的属性。梅森膜散射状态和四夸克分子状态都有四个价值夸克，它们形成了两个颜色中性的簇，我们无法根据可分解的Feynman图中的两个颜色中性簇来区分贡献。 Lucha, Melikhov and Sazdjian assert that the contributions at the order $\mathcal{O}(α_s^k)$ with $k\leq1$ in the operator product expansion, which are factorizable in the color space, are exactly canceled out by the meson-meson scattering states at the hadron side, the tetraquark molecular states begin to receive contributions at the order $ \ MATHCAL {O}（α_s^2）$。这样的断言是值得怀疑的，我们在详细说明中驳斥了主张，并选择轴向向量电流和张量电流来检查断言的结果。经过详细的分析后，我们观察到介子 - 膜散射状态不能饱和QCD和规则，而四夸克分子状态可以饱和QCD总规则。 Landau方程无用于研究四夸克分子状态的QCD总和规则中的Feynman图，tetraquark分子状态开始以$ \ MATHCAL {O}（O}（α_s^0/α_s^1）的顺序接收贡献，而不是以$ \ MATHC $ \ a^2）（a^2）（a）。
The quarks and gluons are confined objects, they cannot be put on the mass-shell, it is questionable to apply the Landau equation to study the Feynman diagrams in the QCD sum rules. Furthermore, we carry out the operator product expansion in the deep Euclidean region $p^2\to -\infty$, where the Landau singularities cannot exist. The Landau equation servers as a kinematical equation in the momentum space, and is independent on the factorizable and nonfactorizable properties of the Feynman diagrams in the color space. The meson-meson scattering state and tetraquark molecular state both have four valence quarks, which form two color-neutral clusters, we cannot distinguish the contributions based on the two color-neutral clusters in the factorizable Feynman diagrams. Lucha, Melikhov and Sazdjian assert that the contributions at the order $\mathcal{O}(α_s^k)$ with $k\leq1$ in the operator product expansion, which are factorizable in the color space, are exactly canceled out by the meson-meson scattering states at the hadron side, the tetraquark molecular states begin to receive contributions at the order $\mathcal{O}(α_s^2)$. Such an assertion is questionable, we refute the assertion in details, and choose an axialvector current and a tensor current to examine the outcome of the assertion. After detailed analysis, we observe that the meson-meson scattering states cannot saturate the QCD sum rules, while the tetraquark molecular states can saturate the QCD sum rules. The Landau equation is of no use to study the Feynman diagrams in the QCD sum rules for the tetraquark molecular states, the tetraquark molecular states begin to receive contributions at the order $\mathcal{O}(α_s^0/α_s^1)$ rather than at the order $\mathcal{O}(α_s^2)$.
