AI 中文总结
本文推导了德西特空间中共形耦合标量场单圈三角形宇宙学关联子的紧致解析公式，其含42个二重对数，无需辅助正则化因子，经数值验证，还揭示了该关联子的数学性质及更高点关联子的研究途径。
AI 中文摘要
我们推导了德西特空间中共形耦合标量场的单圈三角形关联子的紧致解析公式。该结果由六个主导奇点 prefactors 乘以六个能量变量的纯权重二函数构成；它包含42个二重对数，而此前已知的闭式表示中约有120个，且无需辅助正则化因子。这些二重对数以伽罗瓦共轭对形式出现，使得每个贡献在整个物理区域内均为实数。我们通过数值验证了该结果。此外，我们表明其符号可直接从 dressed 积分表示导出，或独立地从朗道奇点和一般一致性条件通过自举得到。最后，我们证明该关联子（在合适归一化下）是每个平方能量的斯蒂尔吉斯函数，且在所有六个平方能量上联合完全单调。这些结构为更高点的单圈宇宙学关联子提供了研究途径。
英文摘要
We derive a compact analytic formula for the one-loop triangle correlator of conformally coupled scalars in de Sitter space. The result is organised as six leading-singularity prefactors multiplying pure weight-two functions of the six energy variables. It contains forty-two dilogarithms, compared with approximately one hundred and twenty in the previously known closed-form representation, and requires no auxiliary regulator. The dilogarithms occur in Galois-conjugate pairs, making each contribution separately real throughout the physical region. We validate the result numerically. Moreover, we show that its symbol can be derived directly from the dressed integral representation or, independently, bootstrapped from Landau singularities and general consistency conditions. Finally, we show that the correlator (in a suitable normalization) is a Stieltjes function of each squared energy separately and is jointly completely monotone in all six squared energies. These structures suggest a route towards higher-point one-loop cosmological correlators.
Comments25 Pages, 5 Figures, 2 Tables
