Four-dimensional differential equations for the leading divergences of dimensionally-regulated loop integrals

Abstract

We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the literature, we show how to find simple differential equations for the divergent part of Feynman integrals. We illustrate the method by an application to heavy quark effective theory at three loops.

arXiv commentthird version with minor changes and two additional supplemental directories

References in corpus (28)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Hopf Algebras, Renormalization and Noncommutative Geometry
• Differential Equations for Feynman Graph Amplitudes
• Dimensionally Regulated One-Loop Integrals
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Towards a Basis for Planar Two-Loop Integrals
• Reducing differential equations for multiloop master integrals
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Iterative structure of finite loop integrals
• A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• The cusp anomalous dimension at three loops and beyond
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Removing infrared divergences from two-loop integrals
• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops