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LINE: Loop Integrals Numerical Evaluation

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arxiv 2501.01943 v1 pith:RG3JXMES submitted 2025-01-03 hep-ph hep-th

LINE: Loop Integrals Numerical Evaluation

classification hep-ph hep-th
keywords evaluationexpansionintegralslinenumericalamplitudesappearboundary
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order ordinary differential equations through series expansion. We have collected these procedures in an open source computer program that we dub \Line{}. Boundary conditions can be provided by the user or computed internally using the method of expansion by regions. Illustrative examples are also given.

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Cited by 10 Pith papers

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

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    hep-ph 2026-07 accept novelty 6.5

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

    hep-ph 2026-06 unverdicted novelty 6.0

    A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.

  5. HyperPrecision: A Mathematica package for High-Precision Numerical Evaluation of Multivariate Hypergeometric Functions

    hep-ph 2026-05 unverdicted novelty 6.0

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    hep-ph 2026-07 accept novelty 5.0

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