arXiv 1201.63642012-01hep-ph

SCET与微扰QCD的阈值重建：分析比较

Threshold resummation in SCET vs. perturbative QCD: an analytic comparison

Marco Bonvini, Stefano Forte, Margherita Ghezzi, Giovanni Ridolfi

备注：: 25 pages, no figures. Final version, to be published in Nucl. Phys. B. Various minor corrections and clarifications; discussion on power counting when tau is far from threshold added at the end of sect 5; Refs [20] and [22] added
DOI：: 10.1016/j.nuclphysb.2012.04.010

摘要：

我们比较阈值remation在QCD中，使用软共线有效理论（SCET），标准微扰QCD形式主义的基础上因式分解和remation的梅林矩的部分子截面。我们认为各种形式的SCET结果，这对应于不同的选择的软规模亩，这种方法的特点。我们推导出一个主公式，涉及SCET重申QCD结果的任何选择的μ_s。然后，我们首先使用它，以表明，如果SCET重建N-Mellin矩空间中进行适当的选择μ_s，它是等价于标准的微扰方法。接下来，我们表明，如果SCET remation是通过选择μ_s的一个部分子动量变量进行的，微扰结果的部分子mummed截面再次重现，但像它的标准微扰对应它是由发散行为的困扰在端点。最后，利用主公式，我们证明了当选择μ s作为强子动量变量时，SCET和标准方法通过一个乘法（卷积）因子联系在一起，该因子包含了对朗道极点和相关发散的依赖。这个因子以一种非普遍的方式依赖于光度;它使图解结果的精度降低了一个对数的幂次，但是如果我们假设光度不包含图解增强项，那么它就是次要的。因此，SCET方法可以变成从微扰结果中去除朗道极点的处方，但为此付出的代价是每一阶精度降低一个对数幂，并且需要对部分子光度做出假设。

英文摘要：

We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET), to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale mu_s that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of mu_s. We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of mu_s it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for mu_s a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but like its standard perturbative counterpart it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when mu_s is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity.

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