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Three-point correlator and pion form factor in quantum chromodynamics: Methods of calculation for two-loop spectral density.

机译：量子色动力学中的三点相关器和介子形式因子：两环光谱密度的计算方法。

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摘要

The methods are developed of two-loop calculation of spectral density for the 3-point correlation function of an electromagnetic current and two axial currents which are the basis of the pion form factor analysis within the framework of QCD sum rules and local quark-hadron duality approach. The nature of various types of contributions is established which are related to particular regions of momentum integrations inside Feynman integrals. The trace factors accompanying all six two-loop diagrams are calculated and classified. To regularize particular loop integrals, the dimensional regularization technique has been used. The calculation involves such methods as infinite-momentum frame approach, alpha-representation method, Sudakov parametrization of the integration momentum and covariant calculation in momentum space. It is shown that final results of integration are given by logarithms and di-logarithm functions. For the diagram with the gluon correction to the electromagnetic vertex, it is shown that its large momentum transfer behavior is dominated by the Feynman mechanism, in which the active quark carries the bulk of the hadron momentum both before and after collision with virtual photon. For this diagram, the Sudakov double logarithmic terms were obtained that are known to convert into the Sudakov form factor after summation over all orders. Another type of double-logarithmic term was found in the contribution of the diagrams with the gluon correction to the axial-current vertices. This term appears as a power correction to the leading power behavior of this diagram governed by a short-distance re-scattering subprocess in which the exchanged gluon has large virtuality. This subprocess corresponds to the asymptotic perturbative QCD contribution. This observation shows that the two double-logarithmic terms have different nature. The methods developed in this dissertation may be applied to other two-loop calculations within the QCD sum rule method.
机译：开发了针对电磁电流和两个轴向电流的三点相关函数的频谱密度的两环计算的方法，这是在QCD和规则和局部夸克-强子对偶性框架内进行离子形式因子分析的基础方法。建立了与费曼积分内部的动量积分的特定区域有关的各种类型的贡献的性质。计算并分类了所有六个两回路图附带的跟踪因子。为了正规化特定的环路积分，已使用了尺寸正规化技术。计算涉及无限动量框架法，α表示法，积分动量的Sudakov参数化以及动量空间的协方差计算等方法。结果表明，积分的最终结果由对数和对数函数给出。对于对电磁顶点进行胶子校正的图表，表明其大的动量传递行为受费曼机制支配，其中主动夸克在与虚拟光子碰撞之前和之后均携带大量强子动量。对于此图，获得了Sudakov双对数项，这些项在对所有阶数求和后已知可以转换为Sudakov形状因数。在带有胶子校正的图表对轴向电流顶点的贡献中，发现了另一种双对数项。该术语似乎是对此图的前导功率行为的功率校正，该功率行为受短距离重新散射子过程的控制，在该过程中，交换的胶子具有较大的虚拟度。该子过程对应于渐近摄动QCD贡献。该观察结果表明，两个双对数项具有不同的性质。本文开发的方法可以应用于QCD求和规则方法中的其他两环计算。

著录项

  • 作者

    Bedir, Islam.;

  • 作者单位

    Old Dominion University.;

  • 授予单位 Old Dominion University.;
  • 学科 Physics Theory.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 249 p.
  • 总页数 249
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 古生物学;
  • 关键词

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