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.

38 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

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