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arXiv 2402.09536hep-ph
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基于Mellin-Barnes展开的次级大质量夸克研究

Secondary massive quarks with the Mellin-Barnes expansion

Alejandro Bris, Vicent Mateu

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61 pages, 17 figures. v2: minimal modifications, journal version
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AI总结：

本研究结合色散积分与Mellin-Barnes展开方法，可直接得到次级夸克大小质量极限下的任意高阶两圈修正展开，复用现有大β₀计算结果，还可推广至有质量规范玻色子修正及RG演化喷注函数的展开计算。

摘要：

树图阶仅涉及无质量或有质量夸克的过程，会从两圈阶开始受到有质量（更轻、更重或等质量）次级夸克的修正，这类修正由虚胶子分裂为有质量夸克反夸克对产生。计算此类两圈修正的一种简便方法是从将虚胶子视为有质量的单圈图入手，对胶子质量进行带有合适核函数的色散积分，即可得到所需的两圈结果。另一方面，Mellin-Barnes表示可用于计算费曼积分按小参数幂次的展开。本文中我们展示如何结合这两种思路，以直接明了的方式得到次级夸克质量在大、小两种极限下的任意高阶展开式。此外，两种展开的收敛半径存在重叠，且两个级数都收敛迅速。我们方法的优势在于，Mellin表示可直接从大β₀计算所需的同一单圈计算中得到完整矩阵元，因此许多已有结果可被复用。只需最小程度的修改，该策略即可应用于计算有质量规范玻色子带来的单圈修正的展开。我们将该方法应用于大量示例，尤其是那些涉及无质量和有质量喷注的因子化截面相关示例，既复现了已知结果，也得到了新结果。我们方法的另一项额外优势是，通过推迟Mellin反演，可得到经重整化群（RG）演化的喷注函数的小质量与大质量展开。在许多情况下，可对级数求和得到闭合表达式。

英文摘要：

Processes involving only massless or massive quarks at tree-level get corrections from massive (lighter, heavier, or equal-mass) secondary quarks starting at two-loop order, generated by a virtual gluon splitting into a massive quark anti-quark pair. One convenient approach to compute such two-loop corrections is starting with the one-loop diagram considering the virtual gluon massive. Carrying out a dispersive integral with a suitable kernel over the gluon mass yields the desired two-loop result. On the other hand, the Mellin-Barnes representation can be used to compute the expansion of Feynman integrals in powers of a small parameter. In this article we show how to combine these two ideas to obtain the corresponding expansions for large and small secondary quark masses to arbitrarily high orders in a straightforward manner. Furthermore, the convergence radius of both expansions can be shown to overlap, being each series rapidly convergent. The advantage of our method is that the Mellin representation is obtained directly for the full matrix element from the same one-loop computation one needs in large-$β_0$ computations, therefore many existing results can be recycled. With minimal modifications, the strategy can be applied to compute the expansion of the one-loop correction coming from a massive gauge boson. We apply this method to a plethora of examples, in particular those relevant for factorized cross sections involving massless and massive jets, recovering known results and obtaining new ones. Another bonus of our approach is that, postponing the Mellin inversion, one can obtain the small- and large-mas expansions for the RG-evolved jet functions. In many cases, the series can be summed up yielding closed expressions.

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