Geometrical methods in loop calculations and the three-point function

Abstract

A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of the kinematical variables is discussed.

6 pages, LaTeX, 3 eps figures, contribution to proceedings of ACAT2005 (Zeuthen, May 2005)

References in corpus (12)

• Dimensionally Regulated Pentagon Integrals
• Dimensionally Regulated One-Loop Integrals
• New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams
• New results for two-loop off-shell three-point diagrams
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• A geometrical angle on Feynman integrals
• A New Hypergeometric Representation of One-Loop Scalar Integrals in $d$ Dimensions
• A Calculational Formalism for One-Loop Integrals
• Application and explicit solution of recurrence relations with respect to space-time dimension
• Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams
• Quark mass dependence of the one-loop three-gluon vertex in arbitrary dimension
• Expansion of massive scalar one-loop integrals to O(ε^2)

Cited by in corpus (22)

• Evaluation of conformal integrals
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• Finding new relationships between hypergeometric functions by evaluating Feynman integrals
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• GKZ-hypergeometric systems for Feynman integrals
• New relationships between Feynman integrals
• Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
• Four-point function in general kinematics through geometrical splitting and reduction
• The system of partial differential equations for the $C_{{}_0}$ function
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• Geometrical splitting and reduction of Feynman diagrams
• Master integrals for $\mathcal{O}(\alpha {\alpha }_s)$ corrections to $H\to Z{Z}^{\ast }$
• Feynman Integrals of Grassmannians
• GKZ-system of the 2-loop self energy with 4 propagators
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• Next-to-next-to-leading order $\mathcal{O}({\alpha }^2{\alpha }_s^2)$ results for top quark pair production in photon--photon collisions: The one-loop squared contributions
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d, II: Special kinematics
• Triangle diagram, Distance Geometry and Symmetries of Feynman Integrals
• A Probabilistic Angle on One Loop Scalar Integrals
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations