发表机构
Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过扩展理想饱和方法并解决Lorentz协方差破坏问题，提出拟合ansätze方案，改进数值点生成与素性检验算法，给出五点振幅新的余维二准素分解。
AI 中文摘要
构造散射振幅中积分系数紧凑表示的一个有效策略是使其奇点结构显式化。这自然可以通过将它们视为多项式商环的分式域中的元素来实现，其中极点对应于代数消没簇。通过部分分式分解进行简化依赖于利用分子的结构，并且至少在初步近似下，由它们在不可约余维二簇上的行为所支配。这些簇可通过相关理想的准素分解来识别。尽管存在通用算法，准素分解在计算上仍然具有挑战性，且通常需要量身定制的策略。在本工作中，我们扩展了一种基于理想饱和的方法，识别了在理想生成元选择中破坏Lorentz协方差的相关问题，并提出了一种基于在特殊运动学极限中拟合ansätze的解决方案。我们还对两种算法进行了实质性改进：一种用于在给定簇附近生成数值点的算法，另一种用于检验无混合理想素性的算法，两者都依赖于计算独立集和簇维数的半数值程序。最后，我们给出了在维度正则化子高次幂下五点无质量振幅的新的余维二准素分解，以及具有五点单有质量运动学的有限余项的分解，其中出现了新的虚假奇点轨迹。
英文摘要
An effective strategy for constructing compact representations of integral coefficients in scattering amplitudes is to make their singularity structure manifest. This is naturally achieved by treating them as elements of fraction fields of polynomial quotient rings, where poles correspond to algebraic vanishing loci. Simplification via partial fraction decomposition relies on exploiting the structure of the numerators and is governed, at least in a first approximation, by their behaviour on irreducible codimension-two varieties. These are identifiable through primary decompositions of the associated ideals. Despite the availability of general algorithms, primary decompositions remain computationally challenging and often require tailored strategies. In this work, we extend an approach based on ideal saturation, identify an issue related to the breaking of Lorentz covariance in the choice of ideal generators, and present a solution based on fitting ansätze in special kinematic limits. We also provide substantial improvements to an algorithm for the generation of numerical points in proximity of given varieties and to one for testing primality of unmixed ideals, both of which rely on a semi-numerical procedure for computing independent sets and variety dimensions. Finally, we present new codimension-two primary decompositions for five-point massless amplitudes at higher powers in the dimensional regulator, and for finite remainders with five-point one-mass kinematics, where a new spurious singular locus appears.
Comments35 pages, 2 figures
