关于单圈宇宙学对撞机信号的数值积分
On the Numerical Integration of One-Loop Cosmological Collider Signals
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中文总结 AI 辅助
针对暴胀单圈双谱中三角形贡献未被探索的问题，提出约化Schwinger方法数值计算一般运动学下的单圈in-in图，首次实现完整单圈双谱的数值评估并构建模板与CMB数据比较。
中文摘要 AI 辅助
在一大类暴胀模型中，主要的非高斯双谱来源于单圈过程而非树图过程。然而，对于唯象学上相关的质量，除最简单的泡泡图之外，现实中的单圈贡献在很大程度上仍未得到探索。这对于观测目的而言是不够的，因为对于一般的质量和耦合，三角形贡献相对于其泡泡对应部分不一定被抑制。我们提出了一种数值方法，用于在全一般的外动量和质量下评估对暴胀双谱有贡献的标量单圈in-in图。首先，Witten-Feynman参数化将de Sitter圈积分约化为由Symanzik图多项式控制的广义Euler-Mellin积分。不幸的是，对于足够重的质量，被积函数中多项式的指数变得复杂，导致使用标准数值技术评估积分时出现符号问题。为了解决这个问题，我们引入了约化Schwinger方法，该方法解析地评估一个高度振荡的子积分以获得Gauss超几何核，将剩余的积分留给标准数值求积。我们通过用${}_3F_2$函数重现树图双谱的已知解析结果来验证该算法，然后将其应用于一般运动学下的单圈泡泡和三角形贡献。这产生了对完整单圈双谱的首次直接数值评估，适用于整个运动学范围。利用这些数值结果，我们构建了双谱模板并将其与CMB数据进行比较。
英文摘要
In a broad class of inflationary models, the leading non-Gaussian bispectrum arises from one-loop rather than tree-level processes. However, realistic one-loop contributions remain largely unexplored for phenomenologically relevant masses beyond the simplest bubble diagrams. This is insufficient for observational purposes because, for generic masses and couplings, triangle contributions need not be suppressed relative to their bubble counterparts. We present a numerical method for evaluating scalar one-loop in-in diagrams contributing to the inflationary bispectrum at fully general external momenta and masses. First, the Witten-Feynman parameterization reduces de Sitter loop integrals to generalized Euler-Mellin integrals governed by Symanzik graph polynomials. Unfortunately, the exponents of the polynomials in the integrand become complex for sufficiently heavy masses, leading to sign problems when evaluating the integral using standard numerical techniques. To remedy this problem, we introduce the reduced Schwinger method, which evaluates a highly oscillatory subintegral analytically to obtain a Gauss hypergeometric kernel, leaving the remaining integrals to standard numerical quadrature. We validate the algorithm by reproducing known analytic results for the tree-level bispectrum in terms of ${}_3F_2$ functions, and then apply it to the one-loop bubble and triangle contributions at general kinematics. This yields the first direct numerical evaluation of the complete one-loop bispectrum, valid across the full kinematic range. Using these numerical results, we construct bispectrum templates and compare them with CMB data.
发表机构
- Institute for Advanced Study（高等研究院）
- MIT Center for Theoretical Physics - a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心-莱因韦伯研究所）
- Center for Cosmology and Particle Physics, New York University（纽约大学宇宙学与粒子物理中心）
- Perimeter Institute for Theoretical Physics（围道理论物理研究所）
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