Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow

Abstract

We proposed a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass flow method. The key of the recipe is to introduce a quadratic term for each linear propagator and then using differential equations to get rid of their effects. As an application, we calculated all master integrals of vacuum integrals containing a gauge link up to four loops, and we checked the results by nontrivial dimensional recurrence relations.

We found a typographical error in our previous code, and thus numerical results in Eq. (30) and the ancillary file are updated

References in corpus (15)

• Lectures on differential equations for Feynman integrals
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Feynman Diagrams and Differential Equations
• Sector Decomposition
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• From loops to trees by-passing Feynman's theorem
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• A Tree-Loop Duality Relation at Two Loops and Beyond
• From multileg loops to trees (by-passing Feynman's Tree Theorem)
• Evaluation of multi-loop multi-scale Feynman integrals for precision physics
• On phase-space integrals with Heaviside functions

Cited by in corpus (12)

• Determining Feynman integrals with only input from linear algebra
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Massive three-loop form factors: anomaly contribution
• Electroweak corrections to double Higgs production at the LHC
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations
• Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
• Four-loop HQET propagators from the DRA method
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• Reclassifying Feynman integrals as special functions