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arXiv 1401.4458hep-ph
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多微分截面：单射流两个角的测量

Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet

Andrew J. Larkoski, Ian Moult, Duff Neill

备注：
43 pages plus appendices, 8 figures. v2 as published in JHEP. minor typos corrected
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摘要：

QCD中微分截面的解析研究通常集中在单个的可观测量上，如质量或推力，并取得了巨大的成功。在这里，我们提出了第一个研究的双差分射流截面考虑两个反冲角测量一个单一的射流。通过分析由两个角定义的相空间，利用软共线有效理论的方法，证明了双微分截面在相空间的边界处分解。我们还表明，在大部分的相空间的截面不能因式分解，只使用软共线模式，排除了一个全球因式分解定理的可能性软共线有效理论。然而，我们能够定义一个简单的插值过程，平滑地连接在一个边界的分解定理到其他。我们提出了一个明确的例子，这在下一个领先的对数精度，并表明插值是唯一的$α_s^4$阶的截面的指数，在合理的假设下。这证明了插值足够稳健，可以将相空间中的所有子空间都考虑到边界因式分解定理的精度。我们比较我们的双微分截面的解析计算的蒙特卡罗模拟，并找到定性的协议。因为我们的论点依赖于相空间的一般结构，我们希望我们的分析将是相关的现象学动机良好的观测量，如$N$ -subjettiness，能量关联函数，平面流的研究。

英文摘要：

The analytic study of differential cross sections in QCD has typically focused on individual observables, such as mass or thrust, to great success. Here, we present a first study of double differential jet cross sections considering two recoil-free angularities measured on a single jet. By analyzing the phase space defined by the two angularities and using methods from soft-collinear effective theory, we prove that the double differential cross section factorizes at the boundaries of the phase space. We also show that the cross section in the bulk of the phase space cannot be factorized using only soft and collinear modes, excluding the possibility of a global factorization theorem in soft-collinear effective theory. Nevertheless, we are able to define a simple interpolation procedure that smoothly connects the factorization theorem at one boundary to the other. We present an explicit example of this at next-to-leading logarithmic accuracy and show that the interpolation is unique up to $α_s^4$ order in the exponent of the cross section, under reasonable assumptions. This is evidence that the interpolation is sufficiently robust to account for all logarithms in the bulk of phase space to the accuracy of the boundary factorization theorem. We compare our analytic calculation of the double differential cross section to Monte Carlo simulation and find qualitative agreement. Because our arguments rely on general structures of the phase space, we expect that much of our analysis would be relevant for the study of phenomenologically well-motivated observables, such as $N$-subjettiness, energy correlation functions, and planar flow.

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