受QCD启发的相对论束缚态模型和介子结构
QCD inspired relativistic bound state model and meson structures
摘要：
本文综合了几种QCD有效哈密顿模型的优点，构造了一个基于QCD的介子束缚态的相对论有效哈密顿模型。基于光阵面QCD有效哈密顿量模型，采用介子平方不变质量算符作为有效哈密顿量。该模型在以下四个方面得到了改进：（1）证明了在质心系和内坐标Hilbert子空间中，介子的总角动量$J$是守恒的，质量本征方程可以用总角动量表象和一组耦合的径向本征方程来表示。（2）在格点量子色动力学结果的基础上，在有效相互作用中引入了相对论性约束势，从而可以很好地描述介子的激发态。（3）唯象地引入SU（3）味混合相互作用来描述味混合介子，质量本征方程包含了不同味组分之间的耦合。（4）质量本征方程是相对论协变性的，径向耦合质量本征方程充分考虑了$L-S $耦合和张量相互作用。用该模型描述了约265个介子的全介子谱。计算的质量，平方半径和衰变常数与数据的协议是相当不错的。对于质量数据具有较大实验不确定性的介子，模型给出了一定的质量值以供检验。对于一些总角动量和宇称没有实验指定的介子，该模型给出了光谱组态$^{2S+1}L_J$的预测。讨论了我们的模型与最近的低能QCD问题--红外共形标度不变性和全息QCD强子模型之间的联系。
英文摘要：
A QCD inspired relativistic effective Hamiltonian model for the bound states of mesons has been constructed, which integrates the advantages of several QCD effective Hamiltonian models. Based on light-front QCD effective Hamiltonian model, the squared invariant mass operator of meson is used as the effective Hamiltonian. The model has been improved significantly in four major aspects: i)it is proved that in center of mass frame and in internal coordinate Hilbert subspace, the total angular momentum $J$ of meson is conserved and the mass eigen equation can be expressed in total angular momentum representation and in terms of a set of coupled radial eigen equations for each $J$. ii)Based on lattice QCD results, a relativistic confining potential is introduced into the effective interaction and the excited states of mesons can be well described. iii)an SU(3) flavor mixing interaction is introduced phenomenologically to describe the flavor mixing mesons and the mass eigen equations contain the coupling among different flavor components. iv)the mass eigen equations are of relativistic covariance and the coupled radial mass eigen equations take full account of $L-S $ coupling and tensor interactions. The model has been applied to describe the whole meson spectra of about 265 mesons with available data. The agreement of the calculated masses, squared radii, and decay constants with data is quite well. For the mesons whose mass data have large experimental uncertainty, the model produces certain mass values for test. For some mesons whose total angular momenta and parity are not assigned experimentally, the model gives a prediction of the spectroscopic configuration$^{2S+1}L_J$. The connection between our model and the recent low energy QCD issues-the infrared conformal scaling invariance and holographic QCD hadron models is discussed.
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