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arXiv 1805.03436hep-phhep-th
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重味QCD中重子的近似哈密顿量

Approximate Hamiltonian for baryons in heavy-flavor QCD

Kamil Serafin, María Gómez-Rocha, Jai More, Stanisław D. Głazek

摘要:

针对强子中胶子的相对论描述,将有效粒子的重整化群方法应用于重夸克QCD中的重子。利用求解RGPEP方程得到的Fock空间哈密顿算符,以耦合常数的二阶幂为基础,提出了重子本征值问题。包含三个夸克和两个或两个以上胶子的本征态分量以在包含一个胶子的分量中插入一个胶子质量项为代价被排除。由此产生的问题减少到等价的一个组件的三个夸克和胶子。由此得到的三个夸克-夸克相互作用项中的每一个都由一个自旋相关的库仑项和一个自旋无关的谐振子项组成。夸克质量的选择是为了最准确地拟合最轻的自旋为1的夸克偶质量。由此产生的估计bbb和ccc状态匹配的估计得到的格点量子色动力学和夸克模型。ccb和bbc国家的质量也被估计。相应的波函数相对于升压是不变的。在ccb态中,魅夸克倾向于形成双夸克。我们的近似哈密顿量的准确性可以通过在相同的方法中包括两个胶子的分量的比较来估计。

英文摘要:

Aiming at relativistic description of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) is applied to baryons in QCD of heavy quarks. The baryon eigenvalue problem is posed using the Fock-space Hamiltonian operator obtained by solving the RGPEP equations up to second order in powers of the coupling constant. The eigenstate components that contain three quarks and two or more gluons are heuristically removed at the price of inserting a gluon-mass term in the component with one gluon. The resulting problem is reduced to the equivalent one for the component of three quarks and no gluons. Each of the three quark-quark interaction terms thus obtained consists of a spin-dependent Coulomb term and a spin-independent harmonic oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia masses most accurately. The resulting estimates for bbb and ccc states match estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc states are also estimated. The corresponding wave functions are invariant with respect to boosts. In the ccb states, charm quarks tend to form diquarks. The accuracy of our approximate Hamiltonian can be estimated through comparison by including components with two gluons within the same method.

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