从隐藏零点到精确分裂与新零点
From Hidden Zeros to Exact Splittings and New Zeros
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中文总结 AI 辅助
本文通过将隐藏零点提升为精确分裂公式，统一了多种振幅结构，并系统发现了五个新的全多重性零点族及连续零点族，深化了对散射振幅约束的理解。
中文摘要 AI 辅助
隐藏零点在散射振幅上施加了超越其常见因子化性质的约束。我们在两个相关方向上探索其结构。首先，我们将隐藏零点提升为显式的分裂公式，这些公式在一般运动学下组织完整振幅。有序的 $\mathrm{Tr}(\phi^3)$ 振幅、非线性西格玛模型（NLSM）振幅以及宇宙学波函数共享相同的定义性精确分裂结构 $\mathcal A=\sum_\alpha R_\alpha\\, {\mathcal J}_{\alpha,L}{\mathcal J}_{\alpha,R} {\mathcal J}_{\alpha,\mathrm{out}}$，该结构适用于任何隐藏零点。每个前因子 $R_\alpha$ 是隐藏零点轨迹的一个条件，因此这种分解逐项显现了隐藏的消失项。其余因子是较低点振幅或流。利用这些表示，我们能够系统地发现超出通常零点之外的新零点轨迹。特别地，我们获得了五个新的全多重性零点族。我们还发现了连续的零点族：其定义方程的系数可以连续变化，而振幅保持为零。
英文摘要
Hidden zeros impose constraints on scattering amplitudes beyond their familiar factorization properties. We explore their structure in two related directions. We first promote hidden zeros to explicit splitting formulas that organize full amplitudes at generic kinematics. Ordered $\mathrm{Tr}(ϕ^3)$ amplitudes, nonlinear sigma model (NLSM) amplitudes, and cosmological wavefunctions share the same defining exact splitting structure $\mathcal A=\sum_αR_α\, {\mathcal J}_{α,L}{\mathcal J}_{α,R} {\mathcal J}_{α,\mathrm{out}}$, adapted to any hidden zero. Each prefactor $R_α$ is a condition of the hidden zero locus, so this decomposition manifests the hidden vanishing term by term. The remaining factors are lower point amplitudes or currents. Using these representations, we can systematically find new zero loci beyond the usual ones. In particular, we obtain five new all-multiplicity zero families. We also find continuous families of zeros: the coefficients of their defining equations can vary continuously while the amplitude remains zero.
发表机构
- University of Groningen（格罗宁根大学）
- Technion – Israel Institute of Technology（以色列理工学院）
- Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
