D介子与O~（++）标胶球的量子色动力学求和规则研究
摘要
本文用量子色动力学求和规则方法研究了0±、1±D介子的质量和耦合常数以及0++标胶球的质量、宽度和耦合常数。
在第一个工作中,我们采用零宽度Gaussian求和规则计算了0±、1±D介子的质量,并给出其耦合常数。首先在fullQCD中和重夸克有效理论框架下采用算符乘积展开得到相应的D介子流的两点函数；再通过Borel变换得到关于D介子流两点函数以及谱函数的Gaussian变换；进而导出了关于D介子的质量与耦合常数的Gaussian求和规则。采用QCD标准的普适输入参数,得到了关于D介子质量和耦合常数与实验值符合得很好的数值结果；其中关于Ds0+(2317)的工作是国际上首次在full QCD中应用QCD求和规则得出的与实验值符合得很好的数值结果：mDs(2317)=2.32±0.13 GeV。
在第二个工作中,我们分别用有限宽度Laplace求和规则与Gaussian求和规则计算了0++标胶球的质量、宽度和耦合常数,令宽度趋于零而自动得到相应的零宽度求和规则结果。在量子色动力学半经典展开的统一框架内,采用瞬子液体模型,我们考虑了纯瞬子场的经典贡献、纯胶子场的量子贡献以及经典瞬子场与量子胶子场之间的相互作用贡献,从而得到0++标胶球的关联函数。采用Breit—Wigner有限宽度共振态模型,用带减除的与未带减除的两种求和规则研究了0++标胶球的性质。为了进一步比较验证,我们将有限宽度趋于0而自洽地得到零宽度求和规则,并重新研究了此标胶球的性质,所得到的关于质量谱的结果与有限宽度的结果基本一致。数值研究结果表明,经典场与量子胶子场之间的相互作用对所考虑的0++标胶球态有较大的贡献。在计算中,我们不仅考虑了计及纯胶子世界QCD直至两圈的贡献和单共振态的情况,而且在计及包含三个手征极限夸克QCD直至三圈的贡献后,对于谱函数分别考虑了单个孤立共振态情况,与2 GcV以下三个标量共振态f0(1370)、f0(1500)和f0(1710)可能存在混合的情况。Laplace求和规则结果表明,0++标胶球的质量可能在f00(1500)共振态处,其质量、宽度和耦合常数分别为m=1.51±0.15 GeV、Γ=0.12±0.04GcV和f=1.55±0.15 GeV：而相应的Gaussian求和规则所给出的0++标胶球的质量、宽度和耦合常数范围分别为m=1.35～1.75 GeV、Γ=0.03～0.60GeV和f=1.35～1.65 GeV。
The properties of 0±、1±D mesons and 0++scalar glueball are investigated by using varies QCD sum rules in this thesis.
In the first work of this thesis, we calculate the masses of 0±、1±D mesons and their couplings to the corresponding currents by using Gaussian sum rules. The forms of the two-point function of D meson current obtained by operator product expansion in heavy-quark effective theory and in full QCD are used. The corresponding Gaussian sum rules for the D mesons are obtained by means of Borel transformation. Based on it, and using the standard QCD input parameters, the masses and the coupling constants of D mesons are then predicted, the results are in good accordance with experimental data. Especially, the mass of DsO+(2317) meson has been obtained first time in full QCD with Gaussian sum rule to be m Ds(2317)= 2.32±0.13 GeV, which is consistent with experimental data.
Our second work is devoted to calculate the mass, width and coupling constant of 0++ scalar glueball in both the finite-width Laplace sum rules and the finite-width Gaussian sum rules. In the framework of a semi-classical expansion for quantum chro-modynamics in the instanton liquid background, the correlation function of the 0++ scalar glueball current is given. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are taken into account as well. Instead of the usual zero-width approximation for the resonance, the Breit-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Laplace sum rules and Gaussian sum rules for the 0++ scalar glueball are derived. For comparison with the zero-width case, we let the width to be zero, and recalculate the mass of 0++ scalar glueball. It turns out that in the zero-width limit, and the results of the finite-width sum rules becomes automatically the corresponding results obtained in the zero-width sum rules. The con-tributions arising from the interactions between instantons and the quantum field are proven to be in-neglectable in 0++ -channel. In calculation, we have not only taken into account the case of quarkless QCD with contributions up to two loops and with a well-isolated lowest resonance, but also the case of QCD with three-light flavors up to three-loop levels with a single resonance below the mass scale of 2 GeV. Furthermore, in consideration of the admixture of f0(1370),f0(1500) and f0(1710) resonances, we have investigated the case of QCD with three massless quarks up to three-loop levels with three lower resonances. The results of Laplace sum rules indicate that the 0++ scalar glueball may lie around f0(1500) resonance, with mass, width and coupling to be m= 1.51±0.15 GeV,Γ= 0.12±0.04 GeV and f= 1.55±0.15 GeV, respectively. The corresponding Gaussian sum rules predict that the ranges of the mass, width and coupling may be m= 1.35～1.75 GeV,Γ= 0.03～0.60 GeV and f= 1.35-1.65 GeV, respectively.
在第一个工作中,我们采用零宽度Gaussian求和规则计算了0±、1±D介子的质量,并给出其耦合常数。首先在fullQCD中和重夸克有效理论框架下采用算符乘积展开得到相应的D介子流的两点函数；再通过Borel变换得到关于D介子流两点函数以及谱函数的Gaussian变换；进而导出了关于D介子的质量与耦合常数的Gaussian求和规则。采用QCD标准的普适输入参数,得到了关于D介子质量和耦合常数与实验值符合得很好的数值结果；其中关于Ds0+(2317)的工作是国际上首次在full QCD中应用QCD求和规则得出的与实验值符合得很好的数值结果：mDs(2317)=2.32±0.13 GeV。
在第二个工作中,我们分别用有限宽度Laplace求和规则与Gaussian求和规则计算了0++标胶球的质量、宽度和耦合常数,令宽度趋于零而自动得到相应的零宽度求和规则结果。在量子色动力学半经典展开的统一框架内,采用瞬子液体模型,我们考虑了纯瞬子场的经典贡献、纯胶子场的量子贡献以及经典瞬子场与量子胶子场之间的相互作用贡献,从而得到0++标胶球的关联函数。采用Breit—Wigner有限宽度共振态模型,用带减除的与未带减除的两种求和规则研究了0++标胶球的性质。为了进一步比较验证,我们将有限宽度趋于0而自洽地得到零宽度求和规则,并重新研究了此标胶球的性质,所得到的关于质量谱的结果与有限宽度的结果基本一致。数值研究结果表明,经典场与量子胶子场之间的相互作用对所考虑的0++标胶球态有较大的贡献。在计算中,我们不仅考虑了计及纯胶子世界QCD直至两圈的贡献和单共振态的情况,而且在计及包含三个手征极限夸克QCD直至三圈的贡献后,对于谱函数分别考虑了单个孤立共振态情况,与2 GcV以下三个标量共振态f0(1370)、f0(1500)和f0(1710)可能存在混合的情况。Laplace求和规则结果表明,0++标胶球的质量可能在f00(1500)共振态处,其质量、宽度和耦合常数分别为m=1.51±0.15 GeV、Γ=0.12±0.04GcV和f=1.55±0.15 GeV：而相应的Gaussian求和规则所给出的0++标胶球的质量、宽度和耦合常数范围分别为m=1.35～1.75 GeV、Γ=0.03～0.60GeV和f=1.35～1.65 GeV。
The properties of 0±、1±D mesons and 0++scalar glueball are investigated by using varies QCD sum rules in this thesis.
In the first work of this thesis, we calculate the masses of 0±、1±D mesons and their couplings to the corresponding currents by using Gaussian sum rules. The forms of the two-point function of D meson current obtained by operator product expansion in heavy-quark effective theory and in full QCD are used. The corresponding Gaussian sum rules for the D mesons are obtained by means of Borel transformation. Based on it, and using the standard QCD input parameters, the masses and the coupling constants of D mesons are then predicted, the results are in good accordance with experimental data. Especially, the mass of DsO+(2317) meson has been obtained first time in full QCD with Gaussian sum rule to be m Ds(2317)= 2.32±0.13 GeV, which is consistent with experimental data.
Our second work is devoted to calculate the mass, width and coupling constant of 0++ scalar glueball in both the finite-width Laplace sum rules and the finite-width Gaussian sum rules. In the framework of a semi-classical expansion for quantum chro-modynamics in the instanton liquid background, the correlation function of the 0++ scalar glueball current is given. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are taken into account as well. Instead of the usual zero-width approximation for the resonance, the Breit-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Laplace sum rules and Gaussian sum rules for the 0++ scalar glueball are derived. For comparison with the zero-width case, we let the width to be zero, and recalculate the mass of 0++ scalar glueball. It turns out that in the zero-width limit, and the results of the finite-width sum rules becomes automatically the corresponding results obtained in the zero-width sum rules. The con-tributions arising from the interactions between instantons and the quantum field are proven to be in-neglectable in 0++ -channel. In calculation, we have not only taken into account the case of quarkless QCD with contributions up to two loops and with a well-isolated lowest resonance, but also the case of QCD with three-light flavors up to three-loop levels with a single resonance below the mass scale of 2 GeV. Furthermore, in consideration of the admixture of f0(1370),f0(1500) and f0(1710) resonances, we have investigated the case of QCD with three massless quarks up to three-loop levels with three lower resonances. The results of Laplace sum rules indicate that the 0++ scalar glueball may lie around f0(1500) resonance, with mass, width and coupling to be m= 1.51±0.15 GeV,Γ= 0.12±0.04 GeV and f= 1.55±0.15 GeV, respectively. The corresponding Gaussian sum rules predict that the ranges of the mass, width and coupling may be m= 1.35～1.75 GeV,Γ= 0.03～0.60 GeV and f= 1.35-1.65 GeV, respectively.
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