大规模三圈形状因子的完整技术：胶子情形
Holonomic techniques for massive 3-loop form factors: the gluonic case
AI总结：
本文针对胶子情形的大质量三圈形状因子，采用大动量方法结合计算机代数与PSLQ搜索，实现了精确解析表示与完整级数展开，为高精度对撞机唯象学提供基准。
AI中文摘要：
矢量、轴矢量、标量和赝标量流的大质量三圈形状因子对于高精度对撞机唯象学至关重要。将夸克框架扩展到更复杂的胶子情形，在参考文献（arXiv:2609.22034 [hep-ph]）中，我们利用先进的计算机代数、自动猜测和大规模PSLQ搜索广泛计算了这些贡献。在此，我们概述了大动量方法的核心策略，并说明了其主要挑战，包括求解创纪录规模的递推关系和微分方程。我们的高精度评估提供了围绕$s=0$的精确解析表示，用MZV表示。我们首次实现了围绕$s=\pm\infty$的完整解析级数展开，该展开依赖于MZV和来自更高数空间的三个常数，以及跨$s \in (-\infty, \infty)$的可靠解析延拓，为现代符号计算树立了里程碑式的基准。
英文摘要：
Massive three-loop form factors for vector, axial-vector, scalar, and pseudoscalar currents are vital for precision collider phenomenology. Extending the quarkonic framework to the more complex gluonic case, in Ref. (arXiv:2609.22034 [hep-ph]) we computed these contributions widely using advanced computer algebra, automated guessing, and large-scale PSLQ searches. Here, we outline the core strategy of the large-moment method and illustrate its main challenges, including solving record-sized recurrences and differential equations. Our high-precision evaluation provides an exact analytic representation around $s=0$ in terms of MZVs. We achieved a complete analytic series expansion around $s=\pm\infty$ for the first time, which depends on MZVs and three constants out of higher number spaces, along with reliable analytic continuations across $s \in (-\infty, \infty)$, serving as a landmark benchmark for modern symbolic computation.
