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arXiv 0910.0625hep-ph
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光阵面全息术与AdS/QCD:对QCD的一种近似

Light-Front Holography and AdS/QCD: A First Approximation to QCD

Stanley J. Brodsky, Guy F. de Téramond

摘要:

将Anti-de Sitter空间(AdS)方法与光阵面全息相结合,得到了介子和重子轻夸克束缚态的谱和波函数的半经典一级近似。从QCD中的束缚态哈密顿运动方程出发,我们导出了用不变的影响变量zeta表示的相对论性光波前方程,该影响变量zeta用来度量强子中夸克和胶子组分在等光波前时间下的分离。这些运动方程在物理时空中等价于描述自旋J模在反de Sitter(AdS)空间中传播的运动方程。它的本征值给出了强子谱,它的本征模代表了给定尺度下强子成分的概率分布。介绍了它在轻介子和重子谱中的应用。预测的介子谱具有弦论Regge形式M^2 = 4 kappa^2(n+L+S/2);即,本征质量的平方在L和n中都是线性的,其中n是径向变量zeta中波函数的节点数。空间类π形状因子也被很好地再现。因此,我们可以得到AdS空间中强子模的描述与在固定光阵面时间的光阵面上量子化的物理时空中QCD的哈密顿表述之间的显著联系。该模型可以通过使用其完整的正交规范解对角化整个QCD光阵面哈密顿量或通过应用Lippmann-Schwinger方法系统地包括QCD相互作用项来系统地改进。

英文摘要:

The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable zeta which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti--de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M^2 = 4 kappa^2(n+L+S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable zeta. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.

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