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Rationalizing roots: an algorithmic approach

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arxiv 1809.10983 v2 pith:DBNYURHR submitted 2018-09-28 hep-th hep-phmath-phmath.MP

Marco Besier , Duco van Straten , Stefan Weinzierl This is my paper · ORCID
classification hep-thhep-phmath-phmath.MP
keywords rootsalgorithmmultiplealgebraicfeynmanhypersurfacepolylogarithmsrationalizing
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abstract

In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which rationalizes the square roots. In this paper, we give an algorithm for rationalizing roots. The algorithm is applicable whenever the algebraic hypersurface associated with the root has a point of multiplicity $(d-1)$, where $d$ is the degree of the algebraic hypersurface. We show that one can use the algorithm iteratively to rationalize multiple roots simultaneously. Several examples from high energy physics are discussed.

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Forward citations

Cited by 4 Pith papers

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

  1. Recursive construction of scalar one-loop integrals in dimensional regularisation

    hep-th 2026-07 conditional novelty 8.0 of 10

    A recursion based on hyperbolic simplex volumes expresses every epsilon-expansion coefficient of scalar one-loop Feynman integrals in terms of multiple polylogarithms.

  2. The spectrum of Feynman-integral geometries at two loops

    hep-th 2025-12 unverdicted novelty 8.0 of 10

    Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.

  3. Electroweak double-box integrals for Moller scattering

    hep-ph 2024-12 conditional novelty 6.0 of 10

    Presents epsilon-factorised master integrals, boundary values, and numerical routines for the planar and non-planar electroweak double-box families relevant to NNLO Moller scattering.

  4. NNLO phase-space integrals for semi-inclusive deep-inelastic scattering

    hep-ph 2024-12 accept novelty 5.0 of 10

    The paper gives closed analytic forms for the 20 phase-space master integrals needed for NNLO semi-inclusive deep-inelastic scattering, using two independent methods that agree with a competing calculation.

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