Multivariate hypergeometric solutions of cosmological (dS) correlators by d log-form differential equations

被引：0
作者：
Jiaqi Chen [1 ]
Bo Feng [2 ]
Yi-Xiao Tao [3 ]
机构：
[1] Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, China University of Petroleum-Beijing, Beijing
[2] Basic Research Center for Energy Interdisciplinary, College of Science, China University of Petroleum-Beijing, Beijing
[3] Beijing Computational Science Research Center, Beijing
[4] Peng Huanwu Center for Fundamental Theory, Anhui, Hefei
[5] Department of Mathematical Sciences, Tsinghua University, Beijing
来源：
Journal of High Energy Physics | / 2025卷 / 3期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
de Sitter space; Early Universe Particle Physics; Scattering Amplitudes;
D O I：
10.1007/JHEP03(2025)075
中图分类号：
学科分类号：
摘要：
In this paper, we give the analytic expression for the homogeneous part of solutions of arbitrary tree-level cosmological correlators, including massive propagators and time-derivative interaction cases. The solutions are given in the form of multivariate hypergeometric functions. It is achieved by two steps. Firstly, we indicate the factorization of the homogeneous part of solutions, i.e., the homogeneous part of solutions of multiple vertices is the product of the solutions of the single vertex. Secondly, we give the solution to the d log-form differential equations of arbitrary single vertex integral family. We also show how to determine the boundary conditions for the differential equations. There are two techniques we developed for the computation. Firstly, we analytically solve d log-form differential equations via power series expansion. Secondly, we handle degenerate multivariate poles in power series expansion of differential equations by blow-up. They could also be useful in the evaluation of multi-loop Feynman integrals in flat spacetime. © The Author(s) 2025.
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