pith. machine review for the scientific record. sign in

arxiv: 1608.01902 · v2 · submitted 2016-08-05 · ✦ hep-ph · hep-th

Recognition: unknown

Scattering amplitudes over finite fields and multivariate functional reconstruction

Authors on Pith no claims yet
classification ✦ hep-ph hep-th
keywords fieldsfinitealgorithmamplitudescalculationsefficientlymultivariatereconstruction
0
0 comments X
read the original abstract

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 6 Pith papers

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

  1. The four-loop non-singlet splitting functions in QCD

    hep-ph 2026-04 unverdicted novelty 8.0

    Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.

  2. The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections

    hep-ph 2026-03 unverdicted novelty 8.0

    N3LO calculation of the B to Xs gamma photon spectrum including complete light-fermion corrections, two massive fermion loops, and large-Nc terms, with improved results in kinetic and MSR mass schemes.

  3. Heavy-Quark Condensate and Vacuum Energy Anomalous Dimension at Five Loops

    hep-ph 2026-05 unverdicted novelty 7.0

    The heavy-quark condensate is computed at five-loop order in QCD with massive quarks, confirming the five-loop vacuum anomalous dimension.

  4. Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit

    hep-ph 2026-05 unverdicted novelty 7.0

    Analytic expressions for the finite remainders of two-loop leading-color helicity amplitudes in Higgs plus two-jet production are obtained in the heavy-top effective theory using numerical unitarity and a new partial-...

  5. Tensor decomposition of $e^+e^-\to\pi^+\pi^-\gamma$ to higher orders in the dimensional regulator

    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.

  6. Next-to-next-to-next-to-leading order QCD corrections to photon-pair production

    hep-ph 2026-04 unverdicted novelty 7.0

    N³LO QCD predictions for photon-pair production are presented, demonstrating perturbative convergence.