QCD求和规则与若干强子结构
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摘要
本文在QCD求和规则的框架内对质量1.5GeV左右标量介子九重态的结构与扭度-3的光锥波函数、最低的标量与赝标量D介子结构作了系统的研究。
按照强子谱给出的信息,质量在1.5GeV左右的轻介子f0(1370)、K0*(1430)、a0(1450)和f0(1500)/f0(1710)构成JP=0+九重态。首先我们的计算表明,在阈值和Borel窗口对每个成员都相同的情况下,通常的求和规则不能得到关于这个多重态成员结构的合理结果。随后在单瞬子近似下,我们在求和规则中加入了相应的瞬子效应,计算结果显示,加入瞬子效应的求和规则可以很好地区分这个多重态,f0(1370)、K0*(1430)和a0(1450)可以在朴素夸克模型的框架内得到很好的解释,f0(1500)具有很大的胶子成分,它们的结构可以表示为：f_0(1370)=(uu+dd)/(?),(1430)=sd,α_0(1450)= (uu-dd)/(?),f_0(1500)=0.9GeV_(ss)+2α_sG_(μν)~αG~(αμν),而f0(1710)的结构还需要深入的分析。
根据本文确定的夸克结构,我们计算了瞬子效应对f0(1370)、K0*(1430)、a0(1450)以及π介子扭度-3的光锥分布幅度的影响。结果表明,这几个介子扭度-3的光锥分布幅度对瞬子密度的大小敏感,在纵向动量分数的某些区间是非正定的,这些波函数对于分析重介子的非轻子衰变具有参考意义。对于可能影响光锥波函数的瞬子效应的其它因素,如真实的瞬子密度、多瞬子效应和非价态贡献等作了初步分析。
从实验可以知道,对于最低态的D介子,JP=0-道双重态质量分裂与夸克模型的预言一致,而JP=0+道的质量分裂与夸克模型预言相反。在QCD求和规则中,作为非微扰修正出现的算符凝聚贡献,一些项是宇称相关的,对于纯轻夸克系统,这样的修正项被压低,然而当重夸克出现时,它们的效应就会有所增强。在原始的QCD求和规则框架内,假设cq结构,我们研究了味SU(3)对称性破缺在实现同一个JP道成员Ds和Dd质量分裂中的作用。计算结果表明,质量效应和宇称相关的非微扰相互作用能够给出正确的D介子质量分裂的趋势：对于0一道,m_D_s-m_D_d-35MeV,0~+道m_D_d-m_D_s-15MeV,这样的质量分裂趋势与实验结果一致。进一步的定性分析可以知道,在0-道,宇称相关的修正项对D。和Dd质量分裂保持一致,导致这一个道质量差比较大；而0+道宇称相关的修正项对Ds和Dd质量差有所抵消,导致这个道质量差较小,这样能对这两个道不同的质量差提供合理的解释。
其它一些相关的话题也作了扼要的讨论。
In this thesis we systematically studied the structure of scalar mesons around 1.5GeV(i.e., K_0~*,α_0 and f_0) as well as the lowest D mesons of 0~- and 0~+ channels in the framework of QCD sum rules approach.
Firstly we gave a systematic description of QCD sum rules approach, in-cluding its principle and necessary mathematical tools. Then we derived the sum rules from light scalar current correlation function. But the results shown that the conventional sum rules can not reveal the realistic mass spectrum of 0+ channel around 1.5GeV. After improving the sum rules by including the instan-ton effects, the masses of scalar meson nonet around 1.5GeV were well separated from each other. The results suggested that f_0(1370), K_0~*(1430) and ao(1450) mesons can be accommodated with the naive quark model, while there is large glueball component inα_0(1500). The underlying structure of f_0(1710) still need further study.
Then based on the suggested structure of f_0(1370), K_0~*(1430),α_0(1450) and pion, we calculated their twist-3 light-cone distribution amplitudes by use of QCD sum rules with inclusion of instanton effects. We found that when the instan-ton involved the twist-3 light-cone distribution amplitudes can develop negative values in some longitudinal momentum fraction range. These instanton-involved twist-3 light-cone distribution amplitudes may be helpful to extract reasonable results in hadronic B decay to mesons mentioned above. We conjectured that the exact instanton density, multi-instantons effect and non-valence contribution may have some impacts on the results which will be implemented in future work.
Finally the mass spitting of multiplet members in 0~- and 0~+ channels of D meson were studied within the framework of conventional QCD sum rules. The results indicated that if we appropriately considered the different role of parity-dependent force induced from the complicated nonperturbative QCD vacuum, which represents itself by parity-dependent condensates in 0~- and 0~+ channels, not only can we give a reasonable explanation to the mass gap of the members in the same channel, but also there will be larger splitting of 0 than 0~+channel. Results also shown that the operator mixing effects was crucial in realizing correct splitting in 0~+members. Generalization to higher states and B mesons were also briefly discussed.
按照强子谱给出的信息,质量在1.5GeV左右的轻介子f0(1370)、K0*(1430)、a0(1450)和f0(1500)/f0(1710)构成JP=0+九重态。首先我们的计算表明,在阈值和Borel窗口对每个成员都相同的情况下,通常的求和规则不能得到关于这个多重态成员结构的合理结果。随后在单瞬子近似下,我们在求和规则中加入了相应的瞬子效应,计算结果显示,加入瞬子效应的求和规则可以很好地区分这个多重态,f0(1370)、K0*(1430)和a0(1450)可以在朴素夸克模型的框架内得到很好的解释,f0(1500)具有很大的胶子成分,它们的结构可以表示为：f_0(1370)=(uu+dd)/(?),(1430)=sd,α_0(1450)= (uu-dd)/(?),f_0(1500)=0.9GeV_(ss)+2α_sG_(μν)~αG~(αμν),而f0(1710)的结构还需要深入的分析。
根据本文确定的夸克结构,我们计算了瞬子效应对f0(1370)、K0*(1430)、a0(1450)以及π介子扭度-3的光锥分布幅度的影响。结果表明,这几个介子扭度-3的光锥分布幅度对瞬子密度的大小敏感,在纵向动量分数的某些区间是非正定的,这些波函数对于分析重介子的非轻子衰变具有参考意义。对于可能影响光锥波函数的瞬子效应的其它因素,如真实的瞬子密度、多瞬子效应和非价态贡献等作了初步分析。
从实验可以知道,对于最低态的D介子,JP=0-道双重态质量分裂与夸克模型的预言一致,而JP=0+道的质量分裂与夸克模型预言相反。在QCD求和规则中,作为非微扰修正出现的算符凝聚贡献,一些项是宇称相关的,对于纯轻夸克系统,这样的修正项被压低,然而当重夸克出现时,它们的效应就会有所增强。在原始的QCD求和规则框架内,假设cq结构,我们研究了味SU(3)对称性破缺在实现同一个JP道成员Ds和Dd质量分裂中的作用。计算结果表明,质量效应和宇称相关的非微扰相互作用能够给出正确的D介子质量分裂的趋势：对于0一道,m_D_s-m_D_d-35MeV,0~+道m_D_d-m_D_s-15MeV,这样的质量分裂趋势与实验结果一致。进一步的定性分析可以知道,在0-道,宇称相关的修正项对D。和Dd质量分裂保持一致,导致这一个道质量差比较大；而0+道宇称相关的修正项对Ds和Dd质量差有所抵消,导致这个道质量差较小,这样能对这两个道不同的质量差提供合理的解释。
其它一些相关的话题也作了扼要的讨论。
In this thesis we systematically studied the structure of scalar mesons around 1.5GeV(i.e., K_0~*,α_0 and f_0) as well as the lowest D mesons of 0~- and 0~+ channels in the framework of QCD sum rules approach.
Firstly we gave a systematic description of QCD sum rules approach, in-cluding its principle and necessary mathematical tools. Then we derived the sum rules from light scalar current correlation function. But the results shown that the conventional sum rules can not reveal the realistic mass spectrum of 0+ channel around 1.5GeV. After improving the sum rules by including the instan-ton effects, the masses of scalar meson nonet around 1.5GeV were well separated from each other. The results suggested that f_0(1370), K_0~*(1430) and ao(1450) mesons can be accommodated with the naive quark model, while there is large glueball component inα_0(1500). The underlying structure of f_0(1710) still need further study.
Then based on the suggested structure of f_0(1370), K_0~*(1430),α_0(1450) and pion, we calculated their twist-3 light-cone distribution amplitudes by use of QCD sum rules with inclusion of instanton effects. We found that when the instan-ton involved the twist-3 light-cone distribution amplitudes can develop negative values in some longitudinal momentum fraction range. These instanton-involved twist-3 light-cone distribution amplitudes may be helpful to extract reasonable results in hadronic B decay to mesons mentioned above. We conjectured that the exact instanton density, multi-instantons effect and non-valence contribution may have some impacts on the results which will be implemented in future work.
Finally the mass spitting of multiplet members in 0~- and 0~+ channels of D meson were studied within the framework of conventional QCD sum rules. The results indicated that if we appropriately considered the different role of parity-dependent force induced from the complicated nonperturbative QCD vacuum, which represents itself by parity-dependent condensates in 0~- and 0~+ channels, not only can we give a reasonable explanation to the mass gap of the members in the same channel, but also there will be larger splitting of 0 than 0~+channel. Results also shown that the operator mixing effects was crucial in realizing correct splitting in 0~+members. Generalization to higher states and B mesons were also briefly discussed.
引文
3本小节主要取自于[8]第一章,关于标准模型更完整的描述可参阅文献[9,10,11,12,13,14,15].
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