组份夸克模型下强子态若干性质的研究
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摘要
强子是最基本的强相互作用系统,正像原子光谱的研究导致量子力学的建立,强子谱的研究给我们带来了夸克模型,进一步促进了强相互作用基本理论-量子色动力学(QCD)的建立。在高能区,QCD具有渐近自由的特性,可以进行微扰计算,计算结果已得到了实验的精确检验。但是在低能区,由于色囚禁,微扰理论不再适用,再加上非微扰QCD理论本身的复杂性,完全从QCD第一原理出发解决低能问题是非常困难的。而强子谱的研究属于QCD的低能领域。现在人们已发展了多种非微扰近似方法：格点规范理论,QCD求和规则,Dyson-Schwinger方程,唯象的夸克模型等。虽然格点QCD,QCD求和规则,Dyson-Schwinger方程等具有很好QCD理论基础的方法,近年来在描述强子性质方面取得了一些重要的进展,但仍然存在一些问题,如难以描述强子的激发态。考虑到低能区QCD具有手征对称性自发破缺的特性,流夸克获得了较大的质量变成组份夸克,组份夸克间通过交换胶子和Goldstone玻色子发生相互作用,人们构造了具有QCD精神的唯象的组份夸克模型。夸克模型在描述强子谱、强子-强子相互作用等方面都取得了非常大的成功,已成为强子物理研究的一个强有力的工具。本文就是在唯象的夸克模型的框架下,对一些强子态的性质开展研究。
关于组份夸克模型中的相对论效应的争论一直伴随着夸克模型的发展。一般认为,对于重夸克系统,相对论效应应该很小,而对于轻夸克系统,相对论效应可能不能忽略,但是强子的质量谱的计算表明,非相对论性的夸克模型能够很好地描述从轻到重的所有夸克系统,虽然对于轻夸克系统其中动能对强子质量的贡献接近甚至超过静止质量对强子质量的贡献。本论文的第一部分工作就是利用我们常用的夸克模型,采用平方囚禁和线性囚禁两种囚禁势,同时在相对论和非相对论动力学中计算了重味夸克偶素bb的能谱、轻子衰变、电磁辐射和强衰变等。结果表明,对于重夸克偶素,两种动力学和两种囚禁势都可以很好地描述其性质。虽然狄拉克动力学的描述整体上要优于薛定谔动力学的描述,但差别不大,所以此时相对论效应确实很小,可以忽略。另外计算结果也表明线形囚禁的描述略优于平方囚禁,特别是对于高激发态。
近年来,BES、BaBar、Belle等实验合作组报道了许多新强子态的发现,如：X(3872)X(3940)Y(4160)Y(4260)Z(4430)等。2005年,BES-Ⅱ在J/ψ→η'π+π-过程中,在η'π+π-的不变质量谱中发现了一个粒子定义为X(1835)。 BES-Ⅲ在相同的过程中,确认了这一发现。在发现这一粒子的同时,还发现了另外两个新的态x(2120)和X(2370)。这些新发现的态都难以用传统的夸克模型来解释。理论上提出了有各种各样的解释,如对X(3872),有正常的粲偶素态、分子态、四夸克系统,重子偶素等解释,对X(1835),同样有η介子的激发态,重子偶素、胶球态和胶球与介子的混合态等解释。在论文的第二部分工作就是在夸克模型的框架下,通过对作为两夸克系统的η和η'以及他们激发态的能谱与强衰变宽度作系统计算,看是否可以将X(1835)X(2120)X(2370)和η(1760)这四个粒子解释为两夸克系统。在计算中,考虑了K介子交换引起的非奇异成分与奇异成分的混合,其混合角由能量计算的动力学确定,衰变计算采用广泛使用的3P0模型,所用到的波函数由能谱计算确定。计算结果表明,对于η(1760),其能量靠近η'(21So),但衰变分支比的计算结果不支持此解释。对于Χ(1835),可以解释为η(41So),衰变宽度的计算也支持这一解释,进一步的实验验证需要测量X(1835)到πa0(980),πa0(1450)的衰变分支比。从质量计算,X(2120)X(2370)在模型中可看作η'(31S0)η'(41S0),但是理论计算得到的衰变宽度远大于实验值。因此将X(2120)和X(2370)解释为η介子的激发态是不合适的。
对新强子态的一个重要研究方面是解释为多夸克系统,例如N(1440)和A(1405)可能是五夸克态。在传统的夸克模型中,认为重子是由三个夸克组成的,介子由夸克-反夸克组成。实际上强子可能的成分应该包含多夸克分量。如介子可能是二夸克(qq),四夸克(q2q-2),夸克-胶子(qqg)等的混合态,重子可能是三夸克(qqq),五夸克(q4q),夸克-胶子(qqqg)等的混合态。为统一描述强子的性质,应该构造包含多夸克和其它成分的夸克模型-非淬火夸克模型。对于介子的非淬火夸克模型已有部分工作。本论文第三部分的工作就是为发展重子的非淬火夸克模型作些初步的尝试。在夸克模型中,考虑五夸克成分,利用3Po模型,计算三夸克与五夸克间的混合,进而得到五夸克成分对重子能量的影响。结果表明,五夸克成分对重子能量有较大的影响。对于基态重子,其影响可以通过调整模型参数来吸收。但对于激发态的重子,调整的参数无法吸收其影响。
Baryons are the basic strong interacting systems. The study of hadron spectrum leads to the emergence of quark model and the establishment of quantum chromodynam-ics (QCD), the fundamental theory of strong interaction, just like the study of atomic spectrum leading to the establishment of quantum mechanics. In high energy region, QCD has a characteristic of asymptotic freedom, the perturbation theory can be applied, the calculated results have been tested precisely by experiments. In low energy region, the perturbation theory fails to work due to the characteristic of QCD, color confinement. So to resolve the problem in low energy region from the first principle is very difficult because of the complicate of QCD. The study of hadron spectrum belongs to the low en-ergy region of QCD. Now various non-perturbation methods lattice QCD, QCD sum rule, Dyson-Schwinger equation, phenomenological quark model and so on, are developed. Al-though the methods based on QCD have made a lot of progresses recently, the description of hadron is still far from satisfactory, e.g., failing to describe the excited states of hadrons. QCD has another characteristic, chiral symmetry spontaneous breaking, because of it, the current quark obtains the dynamical mass and changes into constituent quark. The in-teraction between constituent quarks are introduced by gluon exchange and Goldstone boson exchange. In this way, the "QCD inspired" quark models are constructed. Quark models have achieved a great success in describing hadron spectrum and hadron-hadron interaction. It is am powerful tool in the study of hadron physics. In thesis, we study the properties of hadrons in the framework of quark model.
The argument of the importance of relativistic effects of hadron in quark model per-sists with the development of quark model. Generally, the relativistic effects should be small enough to be neglected for heavy quark system, whereas the effects may not be able to be neglected for light quark system. However, the calculation of non-relativistic quark model shows that it can describe all the hadrons, from light to heavy, well, although the contribution of kinetic energy to the mass of light hadron exceeds the contribution from the rest masses. In this thesis, the constituent quark models with the commonly used po-tentials, quadratic confinement or linear confinement plus one-gluon exchange potential are employed to study bb system with relativistic (Dirac equation) and non-relativistic (Schrodinger equation) dynamics. The calculations of spectrum, electromagnetic decay widths, electromagnetic transition and hadronic decay widths show that two types of dynamics and two types of confinements can describe the heavy quarkonium. The dif-ferences between two dynamics are small, although the description is a little better in Dirac dynamics in the whole. The relativistic effects can be neglected safely for heavy quarkonium. The behavior of linear confinement is also a little better than the quadratic confinement for the highly excited states.
In recent years, a lot of new hadrons are reported by BES, BaBar, Belle and other ex-perimental collaborations, e.g., X(3872),X(3940),Y(4160),Y(4260),Z(4430) and so on. In2005, the BES Collaboration observed a narrow peak in the η'π+π-invariant mass spectrum in the process J/ψ→η'π+π-and define it as X(1835). BES-Ⅲ confirmed it in the same process. Meanwhile, another two new resonances, X(2120) and X(2370), are also observed in the same process. These states are all pseudoscalar meson with I=0. Much work has been devoted to the underlying structures of these states:charmonia, molecular states, four-quark states, baryonium etc. In this work, the pseudoscalar meson spectrum is determined by the chiral quark model. In the mass calculation, the nonstrange mesons and strange mesons are mixed by the K-meson exchange, the mixing angles are determined by the dynamics of the system. Based on the mass spectra of77and77', the possible candidates of X(1835), X(2120), X(2370) and η(1760) are assigned. Then the strong decay widths of the states are calculated in the framework of3P0model, and to see the assignment is reasonable or not by comparing with experimental data. The results show that the assignment of η(1760), X(2120),X(2370) to η'(21S0),η'(31S0),η'(41S0) are disfavored in the present model, whereas the assignment of X(1835) to η(41S0) is possi-ble, to confirm the assignment, the branching ratios of X(1835) to πa0(980),πa0(1450) are needed.
A promising explanation of some new hadron states is the multiquark states, e.g., N(1440) and A(1405) can be explained as pentaquark states. In the traditional quark model, a baryon consists of three quarks and meson consists of quark-antiquark. In reality, a hadron can have multiquark components. For example, a meson is the com-bination of quark-antiquark, diquark-antidiquark, quark-antiquark-gluon and other Fock components, a baryon is the combination of three-quark, four-quark-antiquark, three- quark-gluon and other Fock components. In order to unify the description of hadrons, the unquenched quark model, in which various Fock components are taken into account, should be constructed. In this thesis, the five-quark components are considered in the study of baryon. The mixing between three-quark component and five-quark components are calculated by using3P0model. The mass shift due to the mixing of five-quark compo-nents are obtained. The results show that mass shifts are rather large, especially for the light baryons. For ground state of baryon, the mass shift can be amended by re-adjusting the model parameters. For excited states of baryon, the effects of mass shift may not be absorbed by the parameter re-adjusting.
关于组份夸克模型中的相对论效应的争论一直伴随着夸克模型的发展。一般认为,对于重夸克系统,相对论效应应该很小,而对于轻夸克系统,相对论效应可能不能忽略,但是强子的质量谱的计算表明,非相对论性的夸克模型能够很好地描述从轻到重的所有夸克系统,虽然对于轻夸克系统其中动能对强子质量的贡献接近甚至超过静止质量对强子质量的贡献。本论文的第一部分工作就是利用我们常用的夸克模型,采用平方囚禁和线性囚禁两种囚禁势,同时在相对论和非相对论动力学中计算了重味夸克偶素bb的能谱、轻子衰变、电磁辐射和强衰变等。结果表明,对于重夸克偶素,两种动力学和两种囚禁势都可以很好地描述其性质。虽然狄拉克动力学的描述整体上要优于薛定谔动力学的描述,但差别不大,所以此时相对论效应确实很小,可以忽略。另外计算结果也表明线形囚禁的描述略优于平方囚禁,特别是对于高激发态。
近年来,BES、BaBar、Belle等实验合作组报道了许多新强子态的发现,如：X(3872)X(3940)Y(4160)Y(4260)Z(4430)等。2005年,BES-Ⅱ在J/ψ→η'π+π-过程中,在η'π+π-的不变质量谱中发现了一个粒子定义为X(1835)。 BES-Ⅲ在相同的过程中,确认了这一发现。在发现这一粒子的同时,还发现了另外两个新的态x(2120)和X(2370)。这些新发现的态都难以用传统的夸克模型来解释。理论上提出了有各种各样的解释,如对X(3872),有正常的粲偶素态、分子态、四夸克系统,重子偶素等解释,对X(1835),同样有η介子的激发态,重子偶素、胶球态和胶球与介子的混合态等解释。在论文的第二部分工作就是在夸克模型的框架下,通过对作为两夸克系统的η和η'以及他们激发态的能谱与强衰变宽度作系统计算,看是否可以将X(1835)X(2120)X(2370)和η(1760)这四个粒子解释为两夸克系统。在计算中,考虑了K介子交换引起的非奇异成分与奇异成分的混合,其混合角由能量计算的动力学确定,衰变计算采用广泛使用的3P0模型,所用到的波函数由能谱计算确定。计算结果表明,对于η(1760),其能量靠近η'(21So),但衰变分支比的计算结果不支持此解释。对于Χ(1835),可以解释为η(41So),衰变宽度的计算也支持这一解释,进一步的实验验证需要测量X(1835)到πa0(980),πa0(1450)的衰变分支比。从质量计算,X(2120)X(2370)在模型中可看作η'(31S0)η'(41S0),但是理论计算得到的衰变宽度远大于实验值。因此将X(2120)和X(2370)解释为η介子的激发态是不合适的。
对新强子态的一个重要研究方面是解释为多夸克系统,例如N(1440)和A(1405)可能是五夸克态。在传统的夸克模型中,认为重子是由三个夸克组成的,介子由夸克-反夸克组成。实际上强子可能的成分应该包含多夸克分量。如介子可能是二夸克(qq),四夸克(q2q-2),夸克-胶子(qqg)等的混合态,重子可能是三夸克(qqq),五夸克(q4q),夸克-胶子(qqqg)等的混合态。为统一描述强子的性质,应该构造包含多夸克和其它成分的夸克模型-非淬火夸克模型。对于介子的非淬火夸克模型已有部分工作。本论文第三部分的工作就是为发展重子的非淬火夸克模型作些初步的尝试。在夸克模型中,考虑五夸克成分,利用3Po模型,计算三夸克与五夸克间的混合,进而得到五夸克成分对重子能量的影响。结果表明,五夸克成分对重子能量有较大的影响。对于基态重子,其影响可以通过调整模型参数来吸收。但对于激发态的重子,调整的参数无法吸收其影响。
Baryons are the basic strong interacting systems. The study of hadron spectrum leads to the emergence of quark model and the establishment of quantum chromodynam-ics (QCD), the fundamental theory of strong interaction, just like the study of atomic spectrum leading to the establishment of quantum mechanics. In high energy region, QCD has a characteristic of asymptotic freedom, the perturbation theory can be applied, the calculated results have been tested precisely by experiments. In low energy region, the perturbation theory fails to work due to the characteristic of QCD, color confinement. So to resolve the problem in low energy region from the first principle is very difficult because of the complicate of QCD. The study of hadron spectrum belongs to the low en-ergy region of QCD. Now various non-perturbation methods lattice QCD, QCD sum rule, Dyson-Schwinger equation, phenomenological quark model and so on, are developed. Al-though the methods based on QCD have made a lot of progresses recently, the description of hadron is still far from satisfactory, e.g., failing to describe the excited states of hadrons. QCD has another characteristic, chiral symmetry spontaneous breaking, because of it, the current quark obtains the dynamical mass and changes into constituent quark. The in-teraction between constituent quarks are introduced by gluon exchange and Goldstone boson exchange. In this way, the "QCD inspired" quark models are constructed. Quark models have achieved a great success in describing hadron spectrum and hadron-hadron interaction. It is am powerful tool in the study of hadron physics. In thesis, we study the properties of hadrons in the framework of quark model.
The argument of the importance of relativistic effects of hadron in quark model per-sists with the development of quark model. Generally, the relativistic effects should be small enough to be neglected for heavy quark system, whereas the effects may not be able to be neglected for light quark system. However, the calculation of non-relativistic quark model shows that it can describe all the hadrons, from light to heavy, well, although the contribution of kinetic energy to the mass of light hadron exceeds the contribution from the rest masses. In this thesis, the constituent quark models with the commonly used po-tentials, quadratic confinement or linear confinement plus one-gluon exchange potential are employed to study bb system with relativistic (Dirac equation) and non-relativistic (Schrodinger equation) dynamics. The calculations of spectrum, electromagnetic decay widths, electromagnetic transition and hadronic decay widths show that two types of dynamics and two types of confinements can describe the heavy quarkonium. The dif-ferences between two dynamics are small, although the description is a little better in Dirac dynamics in the whole. The relativistic effects can be neglected safely for heavy quarkonium. The behavior of linear confinement is also a little better than the quadratic confinement for the highly excited states.
In recent years, a lot of new hadrons are reported by BES, BaBar, Belle and other ex-perimental collaborations, e.g., X(3872),X(3940),Y(4160),Y(4260),Z(4430) and so on. In2005, the BES Collaboration observed a narrow peak in the η'π+π-invariant mass spectrum in the process J/ψ→η'π+π-and define it as X(1835). BES-Ⅲ confirmed it in the same process. Meanwhile, another two new resonances, X(2120) and X(2370), are also observed in the same process. These states are all pseudoscalar meson with I=0. Much work has been devoted to the underlying structures of these states:charmonia, molecular states, four-quark states, baryonium etc. In this work, the pseudoscalar meson spectrum is determined by the chiral quark model. In the mass calculation, the nonstrange mesons and strange mesons are mixed by the K-meson exchange, the mixing angles are determined by the dynamics of the system. Based on the mass spectra of77and77', the possible candidates of X(1835), X(2120), X(2370) and η(1760) are assigned. Then the strong decay widths of the states are calculated in the framework of3P0model, and to see the assignment is reasonable or not by comparing with experimental data. The results show that the assignment of η(1760), X(2120),X(2370) to η'(21S0),η'(31S0),η'(41S0) are disfavored in the present model, whereas the assignment of X(1835) to η(41S0) is possi-ble, to confirm the assignment, the branching ratios of X(1835) to πa0(980),πa0(1450) are needed.
A promising explanation of some new hadron states is the multiquark states, e.g., N(1440) and A(1405) can be explained as pentaquark states. In the traditional quark model, a baryon consists of three quarks and meson consists of quark-antiquark. In reality, a hadron can have multiquark components. For example, a meson is the com-bination of quark-antiquark, diquark-antidiquark, quark-antiquark-gluon and other Fock components, a baryon is the combination of three-quark, four-quark-antiquark, three- quark-gluon and other Fock components. In order to unify the description of hadrons, the unquenched quark model, in which various Fock components are taken into account, should be constructed. In this thesis, the five-quark components are considered in the study of baryon. The mixing between three-quark component and five-quark components are calculated by using3P0model. The mass shift due to the mixing of five-quark compo-nents are obtained. The results show that mass shifts are rather large, especially for the light baryons. For ground state of baryon, the mass shift can be amended by re-adjusting the model parameters. For excited states of baryon, the effects of mass shift may not be absorbed by the parameter re-adjusting.
引文
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