Pith. sign in

REVIEW 7 cited by

Constructing d-log integrands and computing master integrals for three-loop four-particle scattering

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2002.09492 v2 pith:S4RWX24J submitted 2020-02-21 hep-ph hep-th

classification hep-phhep-th
keywords integralsalgorithmmasterbasisformsfour-particleintegrandsscattering
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the dimensional regulator up to 8$^{\text{th}}$ power, with coefficients expressed in terms of harmonic polylogarithms. As a basis of master integrals we choose integrals with integrands that only have logarithmic poles - called $d$log forms. This choice greatly facilitates the subsequent computation via the method of differential equations. We detail how this basis is obtained via an improved algorithm originally developed by one of the authors. We provide a public implementation of this algorithm. We explain how the algorithm is naturally applied in the context of unitarity. In addition, we classify our $d$log forms according to their soft and collinear properties.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 7 Pith papers

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

  1. Analytic two-loop amplitudes for $q\bar{q}\to \gamma \gamma$ and $gg \to \gamma \gamma$ mediated by a heavy-quark loop

    hep-ph 2025-01 accept novelty 8.0 of 10

    The two-loop amplitudes for q qbar -> gamma gamma and gg -> gamma gamma with a heavy-quark loop are computed analytically in terms of elliptic iterated integrals, with validated fast series expansions for numerical ev...

  2. Two-loop amplitude for $t\bar{t}W$ production at hadron colliders in the leading colour approximation

    hep-ph 2026-08 conditional novelty 7.0 of 10

    The leading-colour two-loop QCD amplitude for ttbar-W production is evaluated numerically at phase-space points using differential equations and finite-field rational reconstruction.

  3. Differential Equations for Energy Correlators in Any Angle

    hep-ph 2025-06 conditional novelty 7.0 of 10

    A first systematic differential equation framework for any-angle energy correlators in N=4 SYM, with four-point master integrals that include non-polylogarithmic elliptic and hyperelliptic sectors.

  4. Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks

    hep-ph 2026-07 accept novelty 6.5 of 10

    Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.

  5. Notes on the bootstrap of four-point conformal integrals

    hep-th 2026-07 conditional novelty 6.0 of 10

    A leading-singularity bootstrap workflow yields new analytic expressions for four-loop conformal integrals, including previously intractable non-planar sectors.

  6. First look at the evaluation of two-loop Feynman integrals for radiative return processes

    hep-ph 2026-07 accept novelty 6.0 of 10

    Planar two-loop four-point master integrals for massive radiative-return QED, including elliptic and nested-root sectors, are reduced to polynomial-in-ε differential equations that evaluate stably in the physical region.

  7. All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

    hep-ph 2025-12 accept novelty 6.0 of 10

    All nine planar three-loop four-point integral families for two massive external legs are cast into canonical differential equations and evaluated numerically, completing the set needed for leading-colour N3LO diboson...

Pith tools