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arXiv 1003.0576hep-ph
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QCD在$q^2 \bar{q}^{2}$体系中的动力学效应

Dynamical effects of QCD in $q^2 \bar{q}^{2}$ systems

M. Imran Jamil, Bilal Masud

摘要:

本文采用基于纯胶子理论的四夸克势{ \em矩阵}模型研究了四夸克系统与交换介子-介子通道的耦合。我们发现,如果用这种基于最小面积的势矩阵代替以前所用的非对角项胶子场重叠因子$f$的简单高斯形式,则所得到的$T$ -矩阵和相移将产生一种角度依赖性,其分波分析揭示了其中的$D$波和更高的角动量分量。这一新特征表明轨道激发通过极化势影响介子-介子分子性质的可能性。我们采用共振群方法,将动能和重叠矩阵处理在势矩阵的模型上,但通过玻恩近似将所得的复杂积分方程解耦。在这个探索性的研究中,我们使用了二次禁闭,不包括自旋依赖性;我们还使用了相等组分夸克质量的近似。

英文摘要:

We study the coupling of a tetraquark system to an exchanged meson-meson channel, using a pure gluonic theory based four-quark potential {\em matrix} model which is known to fit well a large number of data points for lattice simulations of different geometries of a four-quark system. We find that if this minimal-area-based potential matrix replaces the earlier used simple Gaussian form for the gluon field overlap factor $f$ in its off-diagonal terms, the resulting $T$-matrix and phase shifts develop an angle dependence whose partial wave analysis reveals $D$ wave and higher angular momentum components in it. In addition to the obvious implications of this result for the meson-meson scattering, this new feature indicates the possibility of orbital excitations influencing properties of meson-meson molecules through a polarization potential. We have used a formalism of the resonating group method, treated kinetic energy and overlap matrices on model of the potential matrix, but decoupled the resulting complicated integral equations through the Born approximation. In this exploratory study we have used a quadratic confinement and not included the spin-dependence; we also used the approximation of equal constituent quark masses.

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