A new approach to the momentum expansion of multiloop Feynman diagrams

Abstract

We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the small momentum expansion of an arbitrary diagram. The method is applicable for the expansion w.r.t. all or a subset of external momenta. The coefficients of the expansion are obtained by applying a differential operator to a given integral with shifted value of the space-time dimension $d$ and the expansion momenta set equal to zero. Integrals with changed $d$ are evaluated by using the generalized recurrence relations proposed in \cite{OVT1}. We show how the method works for one- and two-loop integrals. It is also illustrated that our method is simpler and more efficient than others.

16 pages, LaTeX, uses axodraw.sty

References in corpus (4)

• Connection between Feynman integrals having different values of the space-time dimension
• Electroweak corrections to the muon anomalous magnetic moment
• Heavy Quark Vacuum Polarisation to Three Loops
• Tensor reduction of two-loop vacuum diagrams and projectors for expanding three-point functions

Cited by in corpus (24)

• Connection between Feynman integrals having different values of the space-time dimension
• Sector Decomposition
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• Scalar One-Loop Integrals using the Negative-Dimension Approach
• An Approach Toward the Numerical Evaluation of Multi-Loop Feynman Diagrams
• Application of the negative-dimension approach to massless scalar box integrals
• Feynman integrals as A-hypergeometric functions
• Threshold and pseudothreshold values of the sunset diagram
• Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals
• Threshold expansion of the sunset diagram
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Analytic result for the one-loop scalar pentagon integral with massless propagators
• On-shell two-loop three-gluon vertex
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• PV-Reduction of Sunset Topology with Auxiliary Vector
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams
• Evaluating double and triple (?) boxes
• Analytical evaluation of certain on-shell two-loop three-point diagrams
• Generalized Hypergeometric Functions and the Evaluation of Scalar One-loop Integrals in Feynman Diagrams
• LOOL: Mathematica package for evaluating leading order one loop functions
• Massless on-shell box integral with arbitrary powers of propagators