Differential equations for tree--level cosmological correlators with massive states
arXiv:2411.05632 · doi:10.1007/JHEP09(2025)043
Abstract
We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method of differential equations. We explicitly express the internally massive, externally conformally coupled correlator as a power series with respect to a small mass parameter, where the various terms in the series are given by multiple polylogarithms.
43 pages, 6 figures, 4 ancillary files; v2: ciations added, paremeter assumptions modifed and clarifications added; v3: ancillary files updated matches journal version
References in corpus (43)
- Multiloop integrals in dimensional regularization made simple
- Differential Equations for Two-Loop Four-Point Functions
- Numerical evaluation of multiple polylogarithms
- HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
- PolyLogTools - Polylogs for the masses
- Feynman Integrals and Intersection Theory
- A Mellin Space Approach to Cosmological Correlators
- Vector Space of Feynman Integrals and Multivariate Intersection Numbers
- The Cosmological Optical Theorem
- Scattering Amplitudes from Intersection Theory
- Combinatorics and Topology of Kawai-Lewellen-Tye Relations
- Aspects of Scattering Amplitudes and Moduli Space Localization
- Cutting Cosmological Correlators
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Decomposition of Feynman Integrals by Multivariate Intersection Numbers
- Duals of Feynman Integrals, I: Differential Equations
- From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals
- Duals of Feynman Integrals, 2: Generalized Unitarity
- Baikov representations, intersection theory, and canonical Feynman integrals
- The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
- Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
- Constructing Canonical Feynman Integrals with Intersection Theory
- Amplitudes meet Cosmology: A (Scalar) Primer
- Cosmology meets cohomology
- Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
- Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
- Principal Landau Determinants
- Monodromy relations from twisted homology
- Intersection Numbers from Higher-order Partial Differential Equations
- Reduction to master integrals via intersection numbers and polynomial expansions
- On one-loop corrections to the Bunch-Davies wavefunction of the universe
- Correlation functions on the lattice and twisted cocycles
- The Geometry of Cosmological Correlators
- Non-perturbative computation of lattice correlation functions by differential equations
- Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations
- A double copy from twisted (co)homology at genus one
- Real time lattice correlation functions from differential equations
- Self-duality from twisted cohomology
- Multivariate hypergeometric solutions of cosmological (dS) correlators by -form differential equations
- Intersection Numbers from Companion Tensor Algebra
- Twisted Riemann bilinear relations and Feynman integrals
- The recursive structure of Baikov representations II: the top-down reduction with intersection theory
- General Relativity from Intersection Theory