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Fast evaluation of Feynman integrals for Monte Carlo generators

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arxiv 2507.12548 v1 pith:ETYMLUXA submitted 2025-07-16 hep-ph hep-th

Fast evaluation of Feynman integrals for Monte Carlo generators

classification hep-ph hep-th
keywords integralsfeynmanintegratortwo-loopcarlocomplexcomputationaldifferential
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis of integrals in both double and quadruple precision, achieving significantly reduced computational times compared to existing tools. We demonstrate the performance of our integrator by evaluating one- and two-loop five-point Feynman integrals with up to nine complex kinematic scales. In particular, we apply our method to the radiative return process of massive electron-positron annihilation into pions plus an energetic photon within scalar QED, for which we also build the differential equation, and extend it to the case where virtual photons acquire an auxiliary complex mass under the Generalised Vector-Meson Dominance model. Furthermore, we validate our approach on two integral families relevant for the two-loop production of $t\bar{t}+\text{jet}$. The integrator achieves, in double precision, execution times of the order of milliseconds for one-loop topologies and hundreds of milliseconds for the two-loop families, enabling for on-the-fly computation of Feynman integrals in Monte Carlo generators and a more efficient generation of grids for the topologies with prohibitive computational costs.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    hep-ph 2026-04 unverdicted novelty 7.0

    First beyond-NLO tensor decomposition and higher-order analytic one-loop amplitudes for e+e- to pi+pi-gamma, paired with a fast numerical five-point integral evaluator.

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    hep-ph 2026-07 unverdicted novelty 6.0

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  4. Solution of Canonical Differential Equations for Integrals on Arbitrary Geometries

    hep-ph 2026-06 unverdicted novelty 6.0

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    hep-ph 2026-07 accept novelty 5.0

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