光锥分布振幅及其在非微扰QCD中的应用
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摘要
光锥分布振幅不但能够反映强子内部结构的动力学信息,而且是硬遍举过程和光锥求和规则中的基本参量,是光锥求和规则应用当中需要首先解决的问题。本文的主要目的和任务是求解基态八重态重子的光锥分布振幅,以及研究其在光锥求和规则中的应用。
本文给出了基态八重态重子∑±,Λ,Ξ扭曲度至6的光锥分布振幅。我们首先在SU(3)味道对称性近似下,给出基态八重态重子光锥分布振幅的一般定义,并运用各种对称性关系将独立不变分布振幅的个数进行约减；然后利用QCD无质量拉氏量的共形对称性,对分布振幅进行共形分波展开,同时借助于运动方程,将共形展开的系数和一些非微扰的耦合系数联系起来；最后在QCD求和规则框架内定出所需非微扰参数,并给出∑±,Λ,Ξ重子分布振幅的具体形式。在研究当中,我们考虑了SU(3)味道破缺效应对分布振幅的修正,而在做共形展开时,精确到领头阶共形自旋。
本文所得到的光锥分布振幅使得应用光锥求和规则对重子的一些特征参数及相关物理过程进行研究成为可能。作为实例,我们使用光锥求和规则方法计算了∑±,Λ,Ξ重子的电磁形状因子在中等动量转移情况下的物理特性,并利用对其磁形状因子的双极点公式拟合估算了其磁矩；通过计算重重子Λc和Ξc的弱跃迁形状因子,给出了半轻衰变Λc→Λl+vl和Ξc→Ξe+ve过程的衰变宽度和分支比；计算了零动量转移情况下稀有衰变过程Λb→Λγ的相关形状因子,预言了其衰变宽度和分支比。
为看清不同内插流对光锥求和规则的影响,我们应用Ioffe-型内插流计算了相关重子的电磁形状因子及弱跃迁形状因子,并重新估计了Λc和Ξc重子半轻衰变过程的衰变宽度和分支比。我们的计算表明,对于电磁形状因子及磁矩的估计,除了一些特殊情况外,两种内插流并无明显差别。然而对于Λc和Ξc重子的半轻衰变,选择Ioffe-型内插流给出了更为合理的结果。
Light-cone distribution amplitudes of hadrons, which are the fundamental parameters in hard exclusive processes and the light-cone QCD sum rules, contain information of the hadron structure and play an essential role in applications of the light-cone QCD sum rules. The main aims of this thesis are to examine the distribution amplitudes of the octet baryons, and to investigate their applications.
The light-cone distribution amplitudes ofΣ±,ΛandΞbaryons are presented up to twist 6. We first give the general definitions of the octet baryon distribution amplitudes in the SU(3) flavor symmetry limit. The number of the independent distribution amplitudes is reduced with the aid of some symmetry relationships. By considering the conformal symmetry of the massless QCD Lagrangian, the distribution amplitudes are expanded by the conformal partial waves to the leading order of the conformal spin accuracy. With the help of the equation of motion, the coefficients of the conformal expansion are related to some other nonperturbative parameters, which are determined in the framework of QCD sum rules. We then give the explicit expressions of the distribution amplitudes ofΣ±,ΛandΞ. In the calculation, we take into account contributions from SU(3) flavor symmetry breaking effects as corrections.
The distribution amplitudes obtained in this thesis make it possible to study some parameters and physical processes related to the baryons with the light-cone QCD sum rules. As applications, we calculate the electromagnetic form factors ofΣ±, A andΞbaryons in the intermediate momentum transfer. The magnetic moments of the baryons are estimated from the assumption that the magnetic form factors can be fitted by the dipole formula. We also predict the decay widths and branching ratios of the semileptonic decay modesΛc→Λl+vl andΞc→Ξe+ve with the light-cone sum rules of the related weak transition form factors, as well as exclusive rare decay processΛb→Λγ.
In addition, we recalculate the same electromagnetic form factors and the semilep-tonic decay modes with an alternative interpolating currents. Our results show that the choice of the interpolating currents does not lead to obvious difference but for the A baryon, while the Ioffe-type currents give more reliable predictions for the semileptonic decay processes.
本文给出了基态八重态重子∑±,Λ,Ξ扭曲度至6的光锥分布振幅。我们首先在SU(3)味道对称性近似下,给出基态八重态重子光锥分布振幅的一般定义,并运用各种对称性关系将独立不变分布振幅的个数进行约减；然后利用QCD无质量拉氏量的共形对称性,对分布振幅进行共形分波展开,同时借助于运动方程,将共形展开的系数和一些非微扰的耦合系数联系起来；最后在QCD求和规则框架内定出所需非微扰参数,并给出∑±,Λ,Ξ重子分布振幅的具体形式。在研究当中,我们考虑了SU(3)味道破缺效应对分布振幅的修正,而在做共形展开时,精确到领头阶共形自旋。
本文所得到的光锥分布振幅使得应用光锥求和规则对重子的一些特征参数及相关物理过程进行研究成为可能。作为实例,我们使用光锥求和规则方法计算了∑±,Λ,Ξ重子的电磁形状因子在中等动量转移情况下的物理特性,并利用对其磁形状因子的双极点公式拟合估算了其磁矩；通过计算重重子Λc和Ξc的弱跃迁形状因子,给出了半轻衰变Λc→Λl+vl和Ξc→Ξe+ve过程的衰变宽度和分支比；计算了零动量转移情况下稀有衰变过程Λb→Λγ的相关形状因子,预言了其衰变宽度和分支比。
为看清不同内插流对光锥求和规则的影响,我们应用Ioffe-型内插流计算了相关重子的电磁形状因子及弱跃迁形状因子,并重新估计了Λc和Ξc重子半轻衰变过程的衰变宽度和分支比。我们的计算表明,对于电磁形状因子及磁矩的估计,除了一些特殊情况外,两种内插流并无明显差别。然而对于Λc和Ξc重子的半轻衰变,选择Ioffe-型内插流给出了更为合理的结果。
Light-cone distribution amplitudes of hadrons, which are the fundamental parameters in hard exclusive processes and the light-cone QCD sum rules, contain information of the hadron structure and play an essential role in applications of the light-cone QCD sum rules. The main aims of this thesis are to examine the distribution amplitudes of the octet baryons, and to investigate their applications.
The light-cone distribution amplitudes ofΣ±,ΛandΞbaryons are presented up to twist 6. We first give the general definitions of the octet baryon distribution amplitudes in the SU(3) flavor symmetry limit. The number of the independent distribution amplitudes is reduced with the aid of some symmetry relationships. By considering the conformal symmetry of the massless QCD Lagrangian, the distribution amplitudes are expanded by the conformal partial waves to the leading order of the conformal spin accuracy. With the help of the equation of motion, the coefficients of the conformal expansion are related to some other nonperturbative parameters, which are determined in the framework of QCD sum rules. We then give the explicit expressions of the distribution amplitudes ofΣ±,ΛandΞ. In the calculation, we take into account contributions from SU(3) flavor symmetry breaking effects as corrections.
The distribution amplitudes obtained in this thesis make it possible to study some parameters and physical processes related to the baryons with the light-cone QCD sum rules. As applications, we calculate the electromagnetic form factors ofΣ±, A andΞbaryons in the intermediate momentum transfer. The magnetic moments of the baryons are estimated from the assumption that the magnetic form factors can be fitted by the dipole formula. We also predict the decay widths and branching ratios of the semileptonic decay modesΛc→Λl+vl andΞc→Ξe+ve with the light-cone sum rules of the related weak transition form factors, as well as exclusive rare decay processΛb→Λγ.
In addition, we recalculate the same electromagnetic form factors and the semilep-tonic decay modes with an alternative interpolating currents. Our results show that the choice of the interpolating currents does not lead to obvious difference but for the A baryon, while the Ioffe-type currents give more reliable predictions for the semileptonic decay processes.
引文
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