论文标题
n $^2 $ ll的大规模事件形状分布
Massive Event-Shape Distributions at N$^2$LL
论文作者
论文摘要
在最近的一篇论文中，我们展示了如何在完整QCD中最佳计算$ \ Mathcal {o}（α_s）$的大规模事件形状的差分和累积横截面。在本文中，我们通过获取对非恢复敏感的观测值的重新亮相表达式完成研究，以n $^2 $ ll + $ \ $ \ nathcal {o} {o}（α_s）$ precision。我们的结果可用于任何大规模方案中的推力，重型喷射质量和C参数分布，并且很容易被概括为角度和其他事件形状。我们表明，所谓的E-和P-Shemes在共线极限中重合，并计算缺失的零件以达到这种准确性：P-Scheme巨大的喷射功能在软连续性有效理论（SCET）中（SCET）和增强重型夸克有效理论（BHQET）。随后将重新召集的表达式匹配到固定顺序QCD中，以将其有效性扩展到分布的尾巴和远端。喷射函数的计算不能作为前向矩阵元素的不连续性施放，并且涉及$ d = 4-2 \ varepsilon $ dimensions中的相空间积分。我们展示了如何分析求解P-Scheme ocet Jet函数的重新归一化组方程，该方程比其2种杰特的对应物更为复杂，并在各种运动学方面得出了快速的膨胀。最后，当质量效应变得更加相关时，我们进行数值研究以固定。
In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at $\mathcal{O}(α_s)$ in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N$^2$LL + $\mathcal{O}(α_s)$ precision. Our results can be used for thrust, heavy jet mass and C-parameter distributions in any massive scheme, and are easily generalized to angularities and other event shapes. We show that the so-called E- and P-schemes coincide in the collinear limit, and compute the missing pieces to achieve this level of accuracy: the P-scheme massive jet function in Soft-Collinear Effective Theory (SCET) and boosted Heavy Quark Effective Theory (bHQET). The resummed expression is subsequently matched into fixed-order QCD to extend its validity towards the tail and far-tail of the distribution. The computation of the jet function cannot be cast as the discontinuity of a forward-scattering matrix element, and involves phase space integrals in $d=4-2\varepsilon$ dimensions. We show how to analytically solve the renormalization group equation for the P-scheme SCET jet function, which is significantly more complicated than its 2-jettiness counterpart, and derive rapidly-convergent expansions in various kinematic regimes. Finally, we perform a numerical study to pin down when mass effects become more relevant.
