Pith. sign in

REVIEW 8 cited by

Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar t +$jet production at leading colour

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 2503.03603 v2 pith:DJC7BOZM submitted 2025-03-05 hep-th hep-ph

classification hep-thhep-ph
keywords ellipticcanonicalfunctionsrootsfamilyintegralsnestedtwo-loop
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We present differential equations (DEs) in canonical form for a family of two-loop five-point Feynman integrals containing elliptic functions and nested square roots. This is the only family for which canonical DEs were not yet available among those required to compute the two-loop leading-colour amplitude for top-pair production in association with a jet at hadron colliders. We write the DEs in terms of one-forms having (locally) simple poles at all singular points, and highlight the `duplet' structure that generalises the even/odd charge of square roots to nested roots. All transcendental functions in the DEs are expressed in closed form using complete elliptic integrals, while one-forms free of elliptic functions are given in terms of logarithms, including those with the nested roots. In addition to marking a significant step towards next-to-next-to-leading order QCD predictions for an important LHC process, this work represents the first time that a canonical basis of integrals involving elliptic functions has been obtained for a five-particle process.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 8 Pith papers

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

  1. 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.

  2. Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes

    hep-ph 2026-03 accept novelty 7.0 of 10

    First analytic two-loop leading-colour amplitudes for top-Yukawa-induced b bbar H production in the heavy-top limit, with Mathematica and C++ code.

  3. Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons

    hep-th 2025-12 conditional novelty 7.0 of 10

    A general two-loop formula is obtained for all n-point 10d null polygon correlators in planar N=4 SYM, expressed in a conformal-integral basis and verified numerically at 11 points.

  4. Elliptic leading singularities and canonical integrands

    hep-th 2025-04 conditional novelty 7.0 of 10

    A derivative-free elliptic one-form basis yields Feynman integrals whose differential equations have a new factorized form with pure-function solutions.

  5. Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders

    hep-ph 2025-04 conditional novelty 7.0 of 10

    A complete set of two-loop master integrals for leading-colour ttW production is reduced to differential equations that are at most quadratic in the dimensional regulator and evaluated numerically in the physical region.

  6. 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.

  7. 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.

  8. Novel cluster-algebraic letters for 5- and 6-point QCD processes

    hep-th 2026-03 conditional novelty 6.0 of 10

    Candidate symbol alphabets for 5- and 6-point QCD processes are derived from the 9-particle N=4 super Yang-Mills cluster algebra, including new nested square-root letters.

Pith tools