Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour

Abstract

We present the first benchmark evaluation of the two-loop finite remainders for the production of a top-quark pair in association with a jet at hadron colliders in the gluon channel. We work in the leading colour approximation, and perform the numerical evaluation in the physical phase space. To achieve this result, we develop a new method for expressing the master integrals in terms of a (over-complete) basis of special functions that enables the infrared and ultraviolet poles to be cancelled analytically despite the presence of elliptic Feynman integrals. The special function basis makes it manifest that the elliptic functions appear solely in the finite remainder, and can be evaluated numerically through generalised series expansions. The helicity amplitudes are constructed using four dimensional projectors combined with finite-field techniques to perform integration-by-parts reduction, mapping to special functions and Laurent expansion in the dimensional regularisation parameter.

22 pages, 6 figures, 3 tables, ancillary files at https://zenodo.org/records/14473301; v2: published version

References in corpus (14)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• NLO QCD corrections to t tbar + jet production at hadron colliders
• Iterative structure of finite loop integrals
• NNLO QCD corrections to three-photon production at the LHC
• Off-shell Top Quarks with One Jet at the LHC: A comprehensive analysis at NLO QCD
• NNLO QCD corrections to event shapes at the LHC
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• Two-loop massive QCD and QED helicity amplitudes for light-by-light scattering

Cited by in corpus (10)

• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar{t}+$jet production at leading colour
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields
• $\text{history}$: A tool for fully-differential cross sections at next-to-next-to-leading order
• One-Loop QCD Corrections to $\bar{u}d\to t\bar{t}W$ at $\mathcal{O}({\epsilon }^2)$
• One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}({\epsilon }^2)$