η_c电磁产生形状因子的研究

发布时间：2018-04-10 02:00

本文选题：重夸克偶素　切入点：非相对论量子色动力学有效理论　出处：《西南大学》2017年硕士论文

【摘要】：论文基于非相对论量子色动力学有效理论(NRQCD)研究了重夸克偶素产生过程γγ~*→η_c形状因子的相对论修正。NRQCD是一个非常成功的量子色动力学低能有效场论,它可以用来研究重夸克偶素的产生和湮灭过程。NRQCD因子化定理把一个过程因子化成一系列短程系数和长程矩阵元的乘积。其中短程系数包含了标度大于m_Q部分的贡献,而小于此标度的贡献被归入非微扰的长程矩阵元。短程系数可以进行微扰计算,因此可以按耦合常数展开。而各个长程矩阵元是按重夸克偶素系统里面重夸克的特征速度展开的。这样NRQCD因子化公式就把一个产生过程的振幅或者截面按耦合常数和特征速度做双重展开。具体计算到哪一阶需要根据精度要求以及展开级数的收敛性来决定。本论文计算了γγ~*→η_c形状因子领头阶矩阵元对应的短程系数(F)以及次领头阶矩阵元对应的短程系数(G)。其中该过程的F目前在文献已经计算到了两圈图,并结合实验做了唯象讨论。结果表明仅仅考虑相对论修正的领头阶贡献尚不能跟实验取得一致。为了检验NRQCD因子化公式的正确性以及预言能力,利用因子化理论领域常用的匹配方法,本论文研究了该过程的次领头阶矩阵元对应的短程系数G,我们把G计算到微扰展开的次领头阶(也就是一圈图阶)。结合F和G并通过适当的选择输入参数做了详尽的唯象分析和讨论。此外论文也研究了γγ~*→η_b的形状因子,未来实验可以检验理论计算的正确性,从而检验NRQCD理论。论文的计算过程中,利用高能软件包FeynArts生成费曼图并生产费曼振幅;利用FeynCalc进行Dirac矩阵求积、Lorentz指标缩并以及化简表达式;利用Apart和FIRE软件包对圈图振幅进行张量约化;最后一圈图振幅只包含一些简单的标量圈积分,通过计算这些圈积分就最终得到了过程的振幅表达式。为了保证计算的正确性,我们对一些已有经典过程重新进行了计算,这其中包括:J/ψ→e~+e~-,η_c→γγ,e~+e~-→η_cγ的α_s及α_sν~2修正,计算结果与已有文献一致。
[Abstract]:Based on the effective theory of non-relativistic quantum chromodynamics (NRQCD), the relativistic correction of the shape factor of 纬 ~ (纬) ~ (* *) _ (n _ (C)) in heavy quark production is studied. NRQCD is a very successful low-energy effective field theory of quantum chromodynamics.It can be used to study the production and annihilation process of heavy quarkopyne. NRQCD factorization theorem converts a process factor into the product of a series of short-range coefficients and long-range matrix elements.The short-range coefficient includes the contribution of the scale larger than the mQ part of the structure, while the contribution smaller than the scale is classified as the non-perturbation long-range matrix element.The short range coefficient can be calculated by perturbation, so it can be expanded according to the coupling constant.And each long range matrix element is expanded according to the characteristic velocity of heavy quark in heavy quark system.In this way, the NRQCD factorization formula expands the amplitude or cross section of a production process according to the coupling constant and the characteristic velocity.The order to be calculated depends on the accuracy requirement and the convergence of the expansion series.In this paper, we have calculated the short-range coefficients (F) corresponding to the leading matrix elements of the shape factor of 纬 ~ (纬) and 畏 _ c, and the short-range coefficients corresponding to the matrix elements of the sub-leading order.Among them, the F of the process has been calculated in the literature, and the phenomenological discussion has been done in combination with the experiment.The results show that the leading contribution of the relativistic correction is not consistent with the experimental results.In order to verify the correctness of the NRQCD factorization formula and its prediction ability, the matching methods commonly used in the field of factorization theory are used.In this paper, we study the short-range coefficient G corresponding to the sublead matrix element of the process. We calculate G to the sub-leader order of the perturbation expansion (that is, the order of a cycle graph).Combining F and G and selecting appropriate input parameters, the phenomenological analysis and discussion are made in detail.In addition, the shape factor of 纬 -T * * 畏 b is also studied in this paper. The correctness of the theoretical calculation and the NRQCD theory can be verified by future experiments.In the calculation process of the paper, we use the high-energy software package FeynArts to generate the Femannian diagram and produce the Feynman amplitude, use FeynCalc to make the Dirac matrix quadrature Lorentz index shrink and simplify expression, use Apart and FIRE software package to reduce the amplitude of the circle graph by Zhang Liang, and use the software package of Apart and FIRE to reduce the amplitude of cycle graph.The amplitude of the last cycle contains only some simple scalar cycle integrals, and the amplitude expression of the process is obtained by calculating these cycle integrals.In order to ensure the correctness of the calculation, we have recalculated some of the classical processes, including: J / 蠄 e ~ e ~ (-), 畏 _ c / 纬 ~ e ~ (-) ~ E ~ (-) ~ (-) _ _ _
【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】：O572.2

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