Two-loop QCD amplitudes for tt̅W production at the LHC in the leading-colour approximation
Abstract
We present a numerical computation of the two-loop QCD scattering amplitudes for the production of a top-antitop quark pair in association with a W boson (tt̅W) at the LHC in the generalised leading-colour approximation, retaining the exact dependence on the top-quark and W-boson masses. Rather than pursuing a fully analytic calculation, we employ a hybrid framework that combines numerical evaluation with strong algebraic and analytic control, allowing ultraviolet and infrared singularities as well as large intermediate cancellations to be treated exactly. This is achieved by expressing the finite remainder in terms of a set of special functions with rational coefficients. The special functions are evaluated numerically by solving differential equations through power-series expansions, while the values of the rational coefficients are reconstructed, point by point, from finite-field evaluations. The calculation is performed in the 't Hooft-Veltman scheme and validated against an independent implementation in conventional dimensional regularisation employing a substantially different computational strategy. We finally provide the colour- and polarisation-summed hard functions evaluated on the phase-space grid used in a previous computation of the next-to-next-to-leading-order QCD corrections to the tt̅W cross section.
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BibTeX
@misc{becchetti2026twoloop,
title = {{Two-loop QCD amplitudes for $t\bartW$ production at the LHC in the leading-colour approximation}},
author = {Matteo Becchetti and Dhimiter Canko and Xiang Chen and Vsevolod Chestnov and Maximilian Delto and Sara Ditsch and Tiziano Peraro and Mattia Pozzoli and Chiara Savoini and Simone Zoia},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.03746},
eprint = {2608.03746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03746},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-loop QCD amplitudes for tt̅W production at the LHC in the leading-colour approximation
AU - Matteo Becchetti
AU - Dhimiter Canko
AU - Xiang Chen
AU - Vsevolod Chestnov
AU - Maximilian Delto
AU - Sara Ditsch
AU - Tiziano Peraro
AU - Mattia Pozzoli
AU - Chiara Savoini
AU - Simone Zoia
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2608.03746
UR - https://arxiv.org/abs/2608.03746
AB - We present a numerical computation of the two-loop QCD scattering amplitudes for the production of a top-antitop quark pair in association with a W boson (tt̅W) at the LHC in the generalised leading-colour approximation, retaining the exact dependence on the top-quark and W-boson masses. Rather than pursuing a fully analytic calculation, we employ a hybrid framework that combines numerical evaluation with strong algebraic and analytic control, allowing ultraviolet and infrared singularities as well as large intermediate cancellations to be treated exactly. This is achieved by expressing the finite remainder in terms of a set of special functions with rational coefficients. The special functions are evaluated numerically by solving differential equations through power-series expansions, while the values of the rational coefficients are reconstructed, point by point, from finite-field evaluations. The calculation is performed in the 't Hooft-Veltman scheme and validated against an independent implementation in conventional dimensional regularisation employing a substantially different computational strategy. We finally provide the colour- and polarisation-summed hard functions evaluated on the phase-space grid used in a previous computation of the next-to-next-to-leading-order QCD corrections to the tt̅W cross section.
ER -