Dispersive approach in Sudakov resummation
Dispersive approach in Sudakov resummation
复制标题
苏达科夫恢复中的分散方法
DOI：
10.1016/j.nuclphysb.2007.10.022
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
G. Grunberg
中科院分区：
文献类型：
--
作者：
E. Gardi;G. Grunberg
我们给出了QCD中Sudakov重算的色散积分的一般全阶公式。我们表明，Sudakov指数可以写为一个分散积分的谱密度函数，加权的特征功能，编码信息的功率校正。定义了特征函数，并在大β 0极限下进行了解析计算.谱密度函数封装了相互作用的非阿贝尔性质。它们是由特定有效电荷（耦合）的类时不连续性定义的，这些电荷与熟悉的Sudakov反常维度直接相关，并且可以在微扰理论中逐阶计算。色散的方法提供了一个实现的穿着胶子指数，其中Sudakov重新表示增强的内部重新表示的运行耦合校正。我们建立所有的计划不变的博雷尔制定和色散之间的顺序关系，并解决在处理功率校正的差异。我们发现，在背景下的Sudakov再确认的红外有限耦合假设是特别感兴趣的，因为相关的耦合可以被唯一地确定为任何顺序，并可能有一个红外固定点已经在微扰水平。我们证明了这个红外极限是普适的：它是由尖点反常维数决定的。为了说明形式主义，我们讨论了几个例子，包括B介子衰变谱，深非弹性结构函数和Drell-Yan或Higgs生产。
We present a general all-order formulation of Sudakov resummation in QCD in terms of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion integral over spectral density functions, weighted by characteristic functions that encode information on power corrections. The characteristic functions are defined and computed analytically in the large-β0limit. The spectral density functions encapsulate the non-Abelian nature of the interaction. They are defined by the time-like discontinuity of specific effective charges (couplings) that are directly related to the familiar Sudakov anomalous dimensions and can be computed order-by-order in perturbation theory. The dispersive approach provides a realization of dressed gluon exponentiation, where Sudakov resummation is enhanced by an internal resummation of running-coupling corrections. We establish all-order relations between the scheme-invariant Borel formulation and the dispersive one, and address the difference in the treatment of power corrections. We find that in the context of Sudakov resummation the infrared-finite-coupling hypothesis is of special interest because the relevant coupling can be uniquely identified to any order, and may have an infrared fixed point already at the perturbative level. We prove that this infrared limit is universal: it is determined by the cusp anomalous dimension. To illustrate the formalism we discuss a few examples including B-meson decay spectra, deep inelastic structure functions and Drell–Yan or Higgs production.