底夸克偶素的组分夸克模型研究

发布时间：2018-10-11 13:44

【摘要】：正负电子对撞实验观测到一些新的底夸克偶素共振态,而这些新近共振态的发现为从理论上辩识它们的结构提供了机会。量子色动力学(QCD)是目前描述强相互作用的基本理论,其主要特征是渐近自由、手征对称自发破缺和夸克禁闭。由于QCD在高能区的渐近自由,对高能过程可用微扰QCD处理。然而,在低能区,QCD高度非微扰,低能过程需要用非微扰理论处理,而非微扰QCD理论要比微扰QCD理论复杂得多,迄今还没有找到较成熟的处理方法。目前,人们发展了各种低能QCD理论方法,而强子谱也成为检验这些理论方法的有效性提供了重要场所。因此,在夸克模型框架下详细地分析底夸克偶素的质量谱是有意义的。本文采用的组分夸克模型兼备了QCD的渐进自由以及长程禁闭的特点,对强子的基态以及激发态都能给出较好的解释。在短程区域采用单胶子交换势,而在长程部分引入了唯像的线性禁闭势,并基于禁闭的标量和矢量混合属性,给出了其相对论修正。这样得到的夸克—反夸克势除中心力场外,还包括色磁自旋项,自旋-轨道耦合项,自旋相关张量项。在给出势能的形式后,通过数值求解耦合道薛定谔方程,得到基态和激发态的能量以及与能量对应的波函数,并与可用实验数据进行比较。最后,基于数值计算结果,着重分析了由势函数中自旋张量项引起的分波混合效应,讨论了实验上观测分波混合共振的可能性。本文主要分为以下四个部分,在第一部分,本文简要的回顾了强子物理的发展以及简单地介绍了近来常用的非微扰方法。在第二部分,本文详细地介绍了组分夸克模型的基本原理以及数学基础,并给出了非相对论性的组分夸克模型的势。在第三部分,本文利用Fortran程序(FESSDE)计算具有各个量子数的bb?束缚态质量,并将计算结果与bb?束缚态的实验值能谱进行了对比,特别是仔细对比了可能发生S-D波混合的1--态,并附上了各个激发态的波函数的图像,计算了混合态的分波的占比。最后,在附录部分,本文则简单地介绍了FESSDE程序的计算原理。
[Abstract]:Some new bottom quark emitters have been observed in positron collision experiments, and these recent resonance states provide an opportunity to identify their structures theoretically. Quantum chromodynamics (QCD) is a basic theory describing strong interaction at present. Its main characteristics are asymptotic freedom, chiral symmetry spontaneous breaking and quark confinement. Because of the asymptotic freedom of QCD in the high energy region, the perturbation QCD can be used to deal with the high energy process. However, in the low-energy region, the QCD is highly non-perturbation, and the low-energy process needs to be treated by non-perturbation theory, which is much more complicated than the perturbation QCD theory. So far, no more mature treatment method has been found. At present, various low-energy QCD theory methods have been developed, and Hadron spectra have become an important place to test the validity of these theoretical methods. Therefore, it is meaningful to analyze the mass spectrum of bottom quark in detail under the framework of quark model. The component quark model adopted in this paper combines the characteristics of the asymptotic freedom of QCD and the long range confinement. The ground state and excited state of Hadron can be well explained. The single gluon exchange potential is used in the short range region, and the phenomenological linear confinement potential is introduced in the long range region. Based on the scalar and vector mixing properties of the confinement, the relativistic correction is given. In addition to the central force field, the quark-antiquark potential obtained by this method also includes the color magnetic spin term, the spin-orbit coupling term and the spin dependent Zhang Liang term. After giving the form of potential energy, the coupled channel Schrodinger equation is solved numerically. The energy of ground state and excited state and the wave function corresponding to energy are obtained, and compared with the available experimental data. Finally, based on the numerical results, the fractional wave mixing effect caused by the spin Zhang Liang term in the potential function is emphatically analyzed, and the possibility of observing the fractional wave mixing resonance is discussed. This paper is divided into four parts. In the first part, the development of Hadron physics is briefly reviewed and the recent non-perturbation methods are briefly introduced. In the second part, the basic principle and mathematical basis of the component quark model are introduced in detail, and the potential of the nonrelativistic component quark model is given. In the third part, we use the Fortran program (FESSDE) to calculate the bb? with each quantum number. The mass of bound states and the calculated results are compared with those of bb?. The experimental energy spectra of bound states are compared, especially the 1- states where S-D wave mixing may occur are compared carefully, and the images of the wave functions of each excited state are appended to calculate the fractional wave ratio of the mixed states. Finally, in the appendix part, this paper briefly introduces the calculation principle of FESSDE program.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O572.33

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