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arXiv 1202.0814hep-phhep-th
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量子场论中系统处理快度对数的一种形式

A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory

Jui-yu Chiu, Ambar Jain, Duff Neill, Ira Z. Rothstein

摘要:

QCD中的许多观测量依赖于微扰理论的重新确认来保持预测能力。在将截面分解为相关的模态之后,进行恢复。对软反冲效应敏感的一类观测量由于涉及到快度矩阵,所以分解和求和特别具有挑战性。在本文中,我们将提出一种形式主义,它允许一个因式分解和求和的微扰系列,这样的观测系统的方式通过一个“快度重整化群“的概念。也就是说,一个Collin-Soper方程实现为重整化群方程,但具有更普遍的适用性,以观察到的超越传统的横向动量相关的部分子分布函数(TMDPDF)和Sudakov形状因子。这种形式主义的特点是,它允许一个跟踪的(非标准)方案的依赖性,这是固有的任何情况下,其中一个执行一个remation的快度发散。我们提出了一个教学介绍的形式主义,将其应用到著名的大规模Sudakov形状因子。形式主义,然后用来研究当前感兴趣的可观测量。本文给出了Higgs产生的横向动量分布的因式分解定理,并给出了NLL下Higgs产生截面的计算结果。我们的形式允许人们定义规范不变的TMDPDF,这是独立的硬散射振幅和软功能,即他们是uni-tensile的。我们提出了详细的因子分解和remmation的射流加宽截面,包括在pT空间的重整化。此外,我们展示了如何规范和重新规范化的排他性的困扰端点奇点的方式,以允许一个一致的recremation的过程。

英文摘要:

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any scenario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form factor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are uni- versal. We present details of the factorization and resummation of the jet broadening cross section including a renormalization in pT space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

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