非局部量子场论中的四圈希格斯-胶子形状因子
On the Four-Loop Higgs--Gluon Form Factor in Nonlocal Quantum Field Theory
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中文总结 AI 辅助
本文研究非局部量子场论，推导胶子融合希格斯产生的四圈形状因子的闭合施温格参数表示，实现圈动量积分解析计算，为相关对撞机物理研究提供了新方法。
中文摘要 AI 辅助
在粒子物理中，标准模型里胶子融合希格斯产生的虚N³LO贡献需要四圈多尺度QCD振幅，在维数正规化中，这类振幅主要由奇异积分约化和复杂的主积分评估主导。本文中，我们证明非局部紫外完备化可使每个固定阶四圈费曼图在四维空间中完全收敛，同时保留莱曼-西蒙赞齐格曼-齐默曼（LSZ）约化公式所需的解析结构。针对胶子融合过程gg→H，我们推导了闭合形式的施温格参数表示，其中所有圈动量积分均可解析完成，仅留下有限的参数积分可直接数值计算，无需常规的紫外减除。该方法有助于将对撞机硬贡献分离为收敛的四圈形状因子。强耦合常数随后由整函数正规化方案中的有限归一化条件定义，其与overline{MS}耦合常数通过有限匹配关联，匹配后，依赖于调节器的修正会在局域极限E_M→∞时解耦。
英文摘要
In particle physics the virtual N$^3$LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. For gluon-fusion $gg\!\to\!H$ we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the $\overline{\mathrm{MS}}$ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit $E_M\!\to\!\infty$.
