Tropical Feynman integration in the Minkowski regime

Abstract

We present a new computer program, $\text{feyntrop}$, which uses the tropical geometric approach to evaluate Feynman integrals numerically. In order to apply this approach in the physical regime, we introduce a new parametric representation of Feynman integrals that implements the causal $i\epsilon$ prescription concretely while retaining projective invariance. $\text{feyntrop}$ can efficiently evaluate dimensionally regulated, quasi-finite Feynman integrals, with not too exceptional kinematics in the physical regime, with a relatively large number of propagators and with arbitrarily many kinematic scales. We give a systematic classification of all relevant kinematic regimes, review the necessary mathematical details of the tropical Monte Carlo approach, give fast algorithms to evaluate (deformed) Feynman integrands, describe the usage of $\text{feyntrop}$ and discuss many explicit examples of evaluated Feynman integrals.

arXiv comment38 pages, the feyntrop program is available at https://michibo.github.io/feyntrop ; v2: Typos corrected and example section revised. To appear in Computer Physics Communications

References in corpus (29)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• General relativity as an effective field theory: The leading quantum corrections
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Feynman Graph Amplitudes
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Resolution of singularities for multi-loop integrals
• The massless higher-loop two-point function
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• On Motives Associated to Graph Polynomials
• Collider Physics at the Precision Frontier
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Techniques for QCD calculations by numerical integration
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Feynman integrals and hyperlogarithms
• FIESTA5: numerical high-performance Feynman integral evaluation
• Loop Tree Duality for multi-loop numerical integration
• A geometric method of sector decomposition
• Hepp's bound for Feynman graphs and matroids
• Evaluation of multi-loop multi-scale Feynman integrals for precision physics
• Instantons or Renormalons? A Comment on phi4_4 Theory in the MS Scheme
• Cohen-Macaulay Property of Feynman Integrals
• Direct numerical evaluation of multi-loop integrals without contour deformation

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