REVIEW 12 cited by
Canonical differential equations for the elliptic two-loop five-point integral family relevant to tbar 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
Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar t +$jet production at leading colour
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.
Forward citations
Cited by 12 Pith papers
-
Two-loop amplitude for $t\bar{t}W$ production at hadron colliders in the leading colour approximation
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.
-
Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in th...
-
Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes
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.
-
Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
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.
-
Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
-
Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks
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.
-
First look at the evaluation of two-loop Feynman integrals for radiative return processes
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.
-
Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
-
Novel cluster-algebraic letters for 5- and 6-point QCD processes
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.
-
New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
-
One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via ...
-
From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.