arXiv 0710.56932007-10hep-ph

阈值重算到（1-x）中的任意阶

Threshold resummation to any order in (1-x)

Georges Grunberg

备注：: 25 pages; version 2: modified presentation in section 2 and Appendix A, added comments; version 3: incorrect treatment of the longitudinal structure function in (old) Appendix A is suppressed, instead some comments are added in the conclusion section

摘要：

本文以深非弹性散射（F_2（x，Q^2）和F_L（x，Q^2））和Drell-Yan过程为例，对动量空间物理演化核（“物理反常维”）在（1-x）中各阶的阈重定结构提出了一个简单的分析。膨胀中的每一项都与一个不同的重整化群和方案不变的微扰对象（“物理Sudakov反常维度”）相关，这取决于一个单一的动量尺度变量。在展开中的任何顺序，都可以捕获数学上增强的项和常数项。该分析是由一个大的-β_0色散计算。一个色散表示在有限beta_0的物理Sudakov异常尺寸也得到了，与一组'Sudakov有效电荷'封装的非阿贝尔性质的相互作用。发现色散表示需要在（x，Q^2）平面中选择非平凡且依赖于过程的变量。指出了物理Sudakov反常维数的一些有趣性质。随后的矩空间中的1/N展开直接从动量空间展开导出。

英文摘要：

A simple ansatz is suggested for the structure of threshold resummation of the momentum space physical evolution kernels (`physical anomalous dimensions') at all orders in (1-x), taking as examples Deep Inelastic Scattering (F_2(x, Q^2) and F_L(x, Q^2)) and the Drell-Yan process. Each term in the expansion is associated to a distinct renormalization group and scheme invariant perturbative object (`physical Sudakov anomalous dimension') depending on a single momentum scale variable. Both logarithmically enhanced terms and constant terms are captured by the ansatz at any order in the expansion. The ansatz is motivated by a large--beta_0 dispersive calculation. A dispersive representation at finite beta_0 of the physical Sudakov anomalous dimensions is also obtained, associated to a set of `Sudakov effective charges' which encapsulate the non-Abelian nature of the interaction. It is found that the dispersive representation requires a non-trivial, and process-dependent, choice of variables in the (x,Q^2) plane. Some interesting properties of the physical Sudakov anomalous dimensions are pointed out. The ensuing 1/N expansion in moment space is straightforwardly derived from the momentum space expansion.

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英文摘要：

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