- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Higher-Order QCD Corrections to Top-Quark Pair Production in Association with a Jet

Simon Badger* and Colomba Brancaccio†

Matteo Becchetti‡

Michal Czakon§

Heribertus Bayu Hartanto∥

Rene Poncelet

Simone Zoia**

  • Dipartimento di Fisica e Astronomia, Università di Bologna e INFN, Sezione di Bologna, via Irnerio 46, I-40126 Bologna, Italy

  • *Contact author: simondavid.badger@unito.it
  • †Contact author: colomba.brancaccio@unito.it
  • ‡Contact author: matteo.becchetti@unibo.it
  • §Contact author: mczakon@physik.rwth-aachen.de
  • ∥Contact author: bayu.hartanto@apctp.org
  • Contact author: rene.poncelet@ifj.edu.pl
  • **Contact author: simone.zoia@physik.uzh.ch
PDF

Phys. Rev. Lett. 137, 021901 – Published 6 July, 2026

DOI: https://doi.org/10.1103/tv26-7r8g

Abstract

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the standard model of particle physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this Letter, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in quantum chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (62)

  1. J. de Blas, M. Pierini, L. Reina, and L. Silvestrini, Impact of the recent measurements of the top-quark and W-Boson masses on electroweak precision fits, Phys. Rev. Lett. 129, 271801 (2022).
  2. G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, and A. Strumia, Higgs mass and vacuum stability in the Standard Model at NNLO, J. High Energy Phys. 08 (2012) 098.
  3. S. Bailey and L. Harland-Lang, Differential top quark pair production at the LHC: Challenges for PDF fits, Eur. Phys. J. C 80, 60 (2020).
  4. S. Chatrchyan et al. (CMS Collaboration), Determination of the top-quark pole mass and strong coupling constant from the tt¯ production cross section in pp collisions at s=7  TeV, Phys. Lett. B 728, 496 (2014); 738, 526(E) (2014).
  5. A. M. Sirunyan et al. (CMS Collaboration), Measurement of tt¯ normalised multi-differential cross sections in pp collisions at s=13  TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions, Eur. Phys. J. C 80, 658 (2020).
  6. G. Aad et al. (ATLAS Collaboration), Measurement of the energy asymmetry in tt¯j production at 13 TeV with the ATLAS experiment and interpretation in the SMEFT framework, Eur. Phys. J. C 82, 374 (2022).
  7. S. Alioli, P. Fernandez, J. Fuster, A. Irles, S.-O. Moch, P. Uwer, and M. Vos, A new observable to measure the top-quark mass at hadron colliders, Eur. Phys. J. C 73, 2438 (2013).
  8. G. Bevilacqua, H. B. Hartanto, M. Kraus, and M. Worek, Off-shell top quarks with one jet at the LHC: A comprehensive analysis at NLO QCD, J. High Energy Phys. 11 (2016) 098.
  9. J. Fuster, A. Irles, D. Melini, P. Uwer, and M. Vos, Extracting the top-quark running mass using tt¯+1-jet events produced at the Large Hadron Collider, Eur. Phys. J. C 77, 794 (2017).
  10. S. Alioli, J. Fuster, M. V. Garzelli, A. Gavardi, A. Irles, D. Melini, S.-O. Moch, P. Uwer, and K. Voß, Phenomenology of tt¯j+X production at the LHC, J. High Energy Phys. 05 (2022) 146.
  11. S. Chatrchyan et al. (CMS Collaboration), Measurement of jet multiplicity distributions in tt¯ production in pp collisions at s=7  TeV, Eur. Phys. J. C 74, 3014 (2015); 75, 216(E) (2015).
  12. G. Aad et al. (ATLAS Collaboration), Determination of the top-quark pole mass using tt¯+1-jet events collected with the ATLAS experiment in 7 TeV pp collisions, J. High Energy Phys. 10 (2015) 121.
  13. G. Aad et al. (ATLAS Collaboration), Measurement of the top-quark mass in tt¯+1-jet events collected with the ATLAS detector in pp collisions at s=8  TeV, J. High Energy Phys. 11 (2019) 150.
  14. A. Tumasyan et al. (CMS Collaboration), Measurement of the top quark pole mass using tt¯+jet events in the Dilepton final state in proton-proton collisions at s=13  TeV, J. High Energy Phys. 07 (2023) 077.
  15. G. Aad et al. (ATLAS Collaboration), Measurement of the top-quark pole mass in dileptonic tt¯+1-jet events at s=13  TeV with the ATLAS experiment, J. High Energy Phys. 12 (2025) 023.
  16. S. Dittmaier, P. Uwer, and S. Weinzierl, NLO QCD corrections to t anti-t + jet production at hadron colliders, Phys. Rev. Lett. 98, 262002 (2007).
  17. S. Dittmaier, P. Uwer, and S. Weinzierl, Hadronic top-quark pair production in association with a hard jet at next-to-leading order QCD: Phenomenological studies for the Tevatron and the LHC, Eur. Phys. J. C 59, 625 (2009).
  18. C. Gütschow, J. M. Lindert, and M. Schönherr, Multi-jet merged top-pair production including electroweak corrections, Eur. Phys. J. C 78, 317 (2018).
  19. A. Kardos, C. Papadopoulos, and Z. Trocsanyi, Top quark pair production in association with a jet with NLO parton showering, Phys. Lett. B 705, 76 (2011).
  20. S. Alioli, S.-O. Moch, and P. Uwer, Hadronic top-quark pair-production with one jet and parton showering, J. High Energy Phys. 01 (2012) 137.
  21. S. Hoeche, F. Krauss, P. Maierhoefer, S. Pozzorini, M. Schonherr, and F. Siegert, Next-to-leading order QCD predictions for top-quark pair production with up to two jets merged with a parton shower, Phys. Lett. B 748, 74 (2015).
  22. S. Höche, P. Maierhöfer, N. Moretti, S. Pozzorini, and F. Siegert, Next-to-leading order QCD predictions for top-quark pair production with up to three jets, Eur. Phys. J. C 77, 145 (2017).
  23. K. Melnikov and M. Schulze, NLO QCD corrections to top quark pair production in association with one hard jet at hadron colliders, Nucl. Phys. B840, 129 (2010).
  24. K. Melnikov, A. Scharf, and M. Schulze, Top quark pair production in association with a jet: QCD corrections and jet radiation in top quark decays, Phys. Rev. D 85, 054002 (2012).
  25. G. Bevilacqua, H. B. Hartanto, M. Kraus, and M. Worek, Top quark pair production in association with a jet with next-to-leading-order QCD off-shell effects at the large hadron collider, Phys. Rev. Lett. 116, 052003 (2016).
  26. G. Bevilacqua, H. B. Hartanto, M. Kraus, M. Schulze, and M. Worek, Top quark mass studies with tt¯j at the LHC, J. High Energy Phys. 03 (2018) 169.
  27. S. Badger, M. Becchetti, E. Chaubey, and R. Marzucca, Two-loop master integrals for a planar topology contributing to pp→tt¯j, J. High Energy Phys. 01 (2023) 156.
  28. S. Badger, M. Becchetti, N. Giraudo, and S. Zoia, Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation, J. High Energy Phys. 07 (2024) 073.
  29. S. Badger, M. Becchetti, C. Brancaccio, H. B. Hartanto, and S. Zoia, Numerical evaluation of two-loop QCD helicity amplitudes for gg→tt¯g at leading colour, J. High Energy Phys. 03 (2025) 070.
  30. S. Badger, M. Becchetti, C. Brancaccio, M. Czakon, H. B. Hartanto, R. Poncelet, and S. Zoia, Double virtual QCD corrections to tt¯+jet production at the LHC, J. High Energy Phys. 05 (2026) 044.
  31. W. Bernreuther and W. Wetzel, Decoupling of heavy quarks in the minimal subtraction scheme, Nucl. Phys. B197, 228 (1982); B513, 758(E) (1998).
  32. M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693, 259 (2010).
  33. M. Czakon and D. Heymes, Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys. B890, 152 (2014).
  34. M. Czakon, A. van Hameren, A. Mitov, and R. Poncelet, Single-jet inclusive rates with exact color at O(αs4), J. High Energy Phys. 10 (2019) 262.
  35. H. A. Chawdhry, M. L. Czakon, A. Mitov, and R. Poncelet, NNLO QCD corrections to three-photon production at the LHC, J. High Energy Phys. 02 (2020) 057.
  36. H. A. Chawdhry, M. Czakon, A. Mitov, and R. Poncelet, NNLO QCD corrections to diphoton production with an additional jet at the LHC, J. High Energy Phys. 09 (2021) 093.
  37. M. Czakon, A. Mitov, and R. Poncelet, Next-to-next-to-leading order study of three-jet production at the LHC, Phys. Rev. Lett. 127, 152001 (2021); 129, 119901(E) (2022).
  38. H. B. Hartanto, R. Poncelet, A. Popescu, and S. Zoia, Next-to-next-to-leading order QCD corrections to Wbb− production at the LHC, Phys. Rev. D 106, 074016 (2022).
  39. S. Badger, M. Czakon, H. B. Hartanto, R. Moodie, T. Peraro, R. Poncelet, and S. Zoia, Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD, J. High Energy Phys. 10 (2023) 071.
  40. M. Bury and A. van Hameren, Numerical evaluation of multi-gluon amplitudes for High Energy Factorization, Comput. Phys. Commun. 196, 592 (2015).
  41. F. Cascioli, P. Maierhofer, and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108, 111601 (2012).
  42. F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierhöfer, S. Pozzorini, H. Zhang, and M. F. Zoller, OpenLoops 2, Eur. Phys. J. C 79, 866 (2019).
  43. F. Buccioni, S. Pozzorini, and M. Zoller, On-the-fly reduction of open loops, Eur. Phys. J. C 78, 70 (2018).
  44. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, LHAPDF6: Parton density access in the LHC precision era, Eur. Phys. J. C 75, 132 (2015).
  45. R. D. Ball et al. (PDF4LHC Working Group), The PDF4LHC21 combination of global PDF fits for the LHC Run III, J. Phys. G 49, 080501 (2022).
  46. F. J. Tackmann, Beyond scale variations: perturbative theory uncertainties from nuisance parameters, J. High Energy Phys. 08 (2025) 098.
  47. M. A. Lim and R. Poncelet, Robust estimates of theoretical uncertainties at fixed-order in perturbation theory, Phys. Rev. D 112, L111901 (2025).
  48. T. Cridge, G. Marinelli, and F. J. Tackmann, Theory uncertainties in the extraction of αs from Drell-Yan at small transverse momentum, J. High Energy Phys. 12 (2025) 043.

  49. Private communication with Javier Llorente.

  50. M. Czakon, D. Heymes, and A. Mitov, Dynamical scales for multi-TeV top-pair production at the LHC, J. High Energy Phys. 04 (2017) 071.
  51. A. A. Penin, Two-loop corrections to Bhabha scattering, Phys. Rev. Lett. 95, 010408 (2005).
  52. P. Bärnreuther, M. Czakon, and P. Fiedler, Virtual amplitudes and threshold behaviour of hadronic top-quark pair-production cross sections, J. High Energy Phys. 02 (2014) 078.
  53. A. A. Penin, Two-loop photonic corrections to massive Bhabha scattering, Nucl. Phys. B734, 185 (2006).
  54. A. Mitov and S. Moch, The Singular behavior of massive QCD amplitudes, J. High Energy Phys. 05 (2007) 001.
  55. T. Becher and K. Melnikov, Two-loop QED corrections to Bhabha scattering, J. High Energy Phys. 06 (2007) 084.
  56. B. Agarwal, F. Buccioni, F. Devoto, G. Gambuti, A. von Manteuffel, and L. Tancredi, Five-parton scattering in QCD at two loops, Phys. Rev. D 109, 094025 (2024).
  57. G. De Laurentis, H. Ita, and V. Sotnikov, Double-virtual NNLO QCD corrections for five-parton scattering. II. The quark channels, Phys. Rev. D 109, 094024 (2024).
  58. G. De Laurentis, H. Ita, M. Klinkert, and V. Sotnikov, Double-virtual NNLO QCD corrections for five-parton scattering. I. The gluon channel, Phys. Rev. D 109, 094023 (2024).
  59. X. Chen, T. Gehrmann, E. W. N. Glover, A. Huss, B. Mistlberger, and A. Pelloni, Fully differential Higgs boson production to third order in QCD, Phys. Rev. Lett. 127, 072002 (2021).
  60. X. Chen, T. Gehrmann, N. Glover, A. Huss, T.-Z. Yang, and H. X. Zhu, Dilepton rapidity distribution in Drell-Yan production to third order in QCD, Phys. Rev. Lett. 128, 052001 (2022).
  61. X. Chen, T. Gehrmann, E. W. N. Glover, A. Huss, P. F. Monni, E. Re, L. Rottoli, and P. Torrielli, Third-order fiducial predictions for Drell-Yan production at the LHC, Phys. Rev. Lett. 128, 252001 (2022).
  62. X. Chen, T. Gehrmann, N. Glover, A. Huss, T.-Z. Yang, and H. X. Zhu, Transverse mass distribution and charge asymmetry in W boson production to third order in QCD, Phys. Lett. B 840, 137876 (2023).

Outline

Information

Phys. Rev. Lett. 137, 021901– Published 6 July, 2026
  • Received 22 December 2025
  • Revised 24 April 2026
  • Accepted 22 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation