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WH production at the LHC within SMEFT at next-to-next-to-leading order QCD

Marco Bonetti1,2,3,*, Robert V. Harlander3,†, Dmitrii Korneev3,‡, Ming-Ming Long4,§, Kirill Melnikov4,∥, Raoul Röntsch5,6,¶, and Davide Maria Tagliabue4,5,6,**

  • 1Institute for Astroparticle Physics, KIT, D-76344 Eggenstein Leopoldshafen, Germany
  • 2Institute for Theoretical Physics, KIT, D-76128 Karlsruhe, Germany
  • 3Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University, Sommerfeldstrasse 16, D-52056 Aachen, Germany
  • 4Institute for Theoretical Particle Physics, KIT, D-76128 Karlsruhe, Germany
  • 5Tif Lab, Dipartimento di Fisica, Università di Milano, Milan, Italy
  • 6INFN, Sezione di Milano, Via Celoria 16, I-20133 Milan, Italy

  • *Contact author: marco.bonetti@kit.edu
  • †Contact author: harlander@physik.rwth-aachen.de
  • ‡Contact author: kdmitry.de@gmail.com
  • §Contact author: ming-ming.long@kit.edu
  • ∥Contact author: kirill.melnikov@kit.edu
  • Contact author: raoul.rontsch@unimi.it
  • **Contact author: davide.tagliabue@kit.edu
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Phys. Rev. D 112, 034033 – Published 27 August, 2025

DOI: https://doi.org/10.1103/ct5x-hl46

Abstract

We study the impact of the pointlike qq¯′WH interactions originating from a subset of dimension-six operators of the Standard Model effective field theory (SMEFT) on the Higgs boson associated production pp→W+H at the LHC. For consistency, we also take into account the corresponding qq¯′W vertices implied by these operators. We compute the next-to-next-to-leading order quantum chromodynamics (QCD) corrections to this process and compare these corrections in the Standard Model and SMEFT production mechanisms.

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References (71)

  1. R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  2. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  3. W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B268, 621 (1986).
  4. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085.
  5. R. Alonso, E. E. Jenkins, A. V. Manohar, and M. Trott, Renormalization group evolution of the standard model dimension six operators III: Gauge coupling dependence and phenomenology, J. High Energy Phys. 04 (2014) 159.
  6. B. Henning, X. Lu, T. Melia, and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485,…: Higher dimension operators in the SM EFT, J. High Energy Phys. 08 (2017) 016; 09 (2019) 19.
  7. R. V. Harlander, T. Kempkens, and M. C. Schaaf, Standard model effective field theory up to mass dimension 12, Phys. Rev. D 108, 055020 (2023).
  8. J. M. Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100, 242001 (2008).
  9. R. V. Harlander, J. Klappert, C. Pandini, and A. Papaefstathiou, Exploiting the WH/ZH symmetry in the search for new physics, Eur. Phys. J. C 78, 760 (2018).
  10. G. Ferrera, M. Grazzini, and F. Tramontano, Associated WH production at hadron colliders: A fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107, 152003 (2011).
  11. G. Ferrera, M. Grazzini, and F. Tramontano, Higher-order QCD effects for associated WH production and decay at the LHC, J. High Energy Phys. 04 (2014) 039.
  12. G. Ferrera, M. Grazzini, and F. Tramontano, Associated ZH production at hadron colliders: The fully differential NNLO QCD calculation, Phys. Lett. B 740, 51 (2015).
  13. J. M. Campbell, R. K. Ellis, and C. Williams, Associated production of a Higgs boson at NNLO, J. High Energy Phys. 06 (2016) 179.
  14. F. Caola, G. Luisoni, K. Melnikov, and R. Röntsch, NNLO QCD corrections to associated WH production and H→bb¯ decay, Phys. Rev. D 97, 074022 (2018).
  15. G. Ferrera, G. Somogyi, and F. Tramontano, Associated production of a Higgs boson decaying into bottom quarks at the LHC in full NNLO QCD, Phys. Lett. B 780, 346 (2018).
  16. R. Gauld, A. Gehrmann-De Ridder, E. W. N. Glover, A. Huss, and I. Majer, Associated production of a Higgs boson decaying into bottom quarks and a weak vector boson decaying leptonically at NNLO in QCD, J. High Energy Phys. 10 (2019) 002.
  17. M. L. Ciccolini, S. Dittmaier, and M. Krämer, Electroweak radiative corrections to associated WH and ZH production at hadron colliders, Phys. Rev. D 68, 073003 (2003).
  18. A. Denner, S. Dittmaier, S. Kallweit, and A. Mück, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, J. High Energy Phys. 03 (2012) 075.
  19. A. Denner, S. Dittmaier, S. Kallweit, and A. Mück, HAWK 2.0: A Monte Carlo program for Higgs production in vector-boson fusion and Higgs strahlung at hadron colliders, Comput. Phys. Commun. 195, 161 (2015).
  20. J. Baglio, C. Duhr, B. Mistlberger, and R. Szafron, Inclusive production cross sections at N3LO, J. High Energy Phys. 12 (2022) 066.
  21. S. Alioli, W. Dekens, M. Girard, and E. Mereghetti, NLO QCD corrections to SM-EFT dilepton and electroweak Higgs boson production, matched to parton shower in POWHEG, J. High Energy Phys. 08 (2018) 205.
  22. W. Bizoń, F. Caola, K. Melnikov, and R. Röntsch, Anomalous couplings in associated VH production with Higgs boson decay to massive b quarks at NNLO in QCD, Phys. Rev. D 105, 014023 (2022).
  23. U. Haisch, D. J. Scott, M. Wiesemann, G. Zanderighi, and S. Zanoli, NNLO event generation for pp→Zh→ℓ+ℓ−bb¯ production in the SM effective field theory, J. High Energy Phys. 07 (2022) 054.
  24. R. Franceschini, G. Panico, A. Pomarol, F. Riva, and A. Wulzer, Electroweak precision tests in high-energy diboson processes, J. High Energy Phys. 02 (2018) 111.
  25. R. Gauld, U. Haisch, and L. Schnell, SMEFT at NNLO+PS: Vh production, J. High Energy Phys. 01 (2024) 192.
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ct5x-hl46 for expressions for the two-loop, one-loop, and tree-level amplitudes used in this paper.
  27. A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek, and K. Suxho, Feynman rules for the standard model effective field theory in Rξ-gauges, J. High Energy Phys. 06 (2017) 143.
  28. J. ter Hoeve, L. Mantani, A. N. Rossia, J. Rojo, and E. Vryonidou, Connecting scales: RGE effects in the SMEFT at the LHC and future colliders, J. High Energy Phys. 06 (2025) 125.
  29. E. d. S. Almeida, A. Alves, O. J. P. Éboli, and M. C. Gonzalez-Garcia, Electroweak legacy of the LHC run II, Phys. Rev. D 105, 013006 (2022).
  30. J. Kley, T. Theil, E. Venturini, and A. Weiler, Electric dipole moments at one-loop in the dimension-6 SMEFT, Eur. Phys. J. C 82, 926 (2022).
  31. R. Boughezal, E. Mereghetti, and F. Petriello, Dilepton production in the SMEFT at O(1/Λ4), Phys. Rev. D 104, 095022 (2021).
  32. O. Brein, R. Harlander, M. Wiesemann, and T. Zirke, Top-quark mediated effects in hadronic Higgs-strahlung, Eur. Phys. J. C 72, 1868 (2012).
  33. B. A. Kniehl, Associated production of Higgs and Z bosons from gluon fusion in hadron collisions, Phys. Rev. D 42, 2253 (1990).
  34. O. Brein, A. Djouadi, and R. Harlander, NNLO QCD corrections to the Higgs-Strahlung processes at hadron colliders, Phys. Lett. B 579, 149 (2004).
  35. H. Elvang and Y.-t. Huang, Scattering amplitudes, arXiv:1308.1697.
  36. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105, 279 (1993).
  37. B. Ruijl, T. Ueda, and J. Vermaseren, form version 4.2, arXiv:1707.06453.
  38. W. R. Inc., Mathematica, Version 13.0, Champaign, IL, 2024, https://www.wolfram.com/mathematica.
  39. L. W. Garland, T. Gehrmann, E. W. N. Glover, A. Koukoutsakis, and E. Remiddi, Two loop QCD helicity amplitudes for e+e−→three jets, Nucl. Phys. B642, 227 (2002).
  40. T. Gehrmann, E. W. N. Glover, T. Huber, N. Ikizlerli, and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, J. High Energy Phys. 06 (2010) 094.
  41. K. G. Chetyrkin and F. V. Tkachov, Integration by parts: The algorithm to calculate β functions in 4 loops, Nucl. Phys. B192, 159 (1981).
  42. S. Laporta, High-precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15, 5087 (2000).
  43. A. von Manteuffel and C. Studerus, reduze 2—Distributed Feynman integral reduction, arXiv:1201.4330.
  44. P. Maierhöfer, J. Usovitsch, and P. Uwer, kira—A Feynman integral reduction program, Comput. Phys. Commun. 230, 99 (2018).
  45. J. Klappert, F. Lange, P. Maierhöfer, and J. Usovitsch, Integral reduction with kira 2.0 and finite field methods, Comput. Phys. Commun. 266, 108024 (2021).
  46. R. H. Lewis, Fermat: A computer algebra system for polynomial and matrix multiplication, computer Software, https://home.bway.net/lewis.
  47. J. Klappert and F. Lange, Reconstructing rational functions with firefly, Comput. Phys. Commun. 247, 106951 (2020).
  48. J. Klappert, S. Y. Klein, and F. Lange, Interpolation of dense and sparse rational functions and other improvements in firefly, Comput. Phys. Commun. 264, 107968 (2021).
  49. T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B580, 485 (2000).
  50. S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427, 161 (1998).
  51. G. Passarino and M. J. G. Veltman, One loop corrections for e+e− annihilation into μ+μ− in the Weinberg model, Nucl. Phys. B160, 151 (1979).
  52. 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).
  53. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079.
  54. G. Cullen, N. Greiner, G. Heinrich, G. Luisoni, P. Mastrolia, G. Ossola, T. Reiter, and F. Tramontano (gosam Collaboration), Automated one-loop calculations with gosam, Eur. Phys. J. C 72, 1889 (2012).
  55. G. Cullen et al. (gosam Collaboration), gosam-2.0: A tool for automated one-loop calculations within the standard model and beyond, Eur. Phys. J. C 74, 3001 (2014).
  56. T. Peraro, finiteflow: Multivariate functional reconstruction using finite fields and dataflow graphs, J. High Energy Phys. 07 (2019) 031.
  57. T. Gehrmann and E. Remiddi, Two loop master integrals for γ*→3 jets: The planar topologies, Nucl. Phys. B601, 248 (2001).
  58. T. Gehrmann and E. Remiddi, Two loop master integrals for γ*→3 jets: The nonplanar topologies, Nucl. Phys. B601, 287 (2001).
  59. O. Brein, R. V. Harlander, and T. J. E. Zirke, vh@nnlo—Higgs strahlung at hadron colliders, Comput. Phys. Commun. 184, 998 (2013).
  60. R. Boughezal, J. M. Campbell, R. K. Ellis, C. Focke, W. Giele, X. Liu, F. Petriello, and C. Williams, Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77, 7 (2017).
  61. F. Caola, K. Melnikov, and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J. C 77, 248 (2017).
  62. F. Caola, K. Melnikov, and R. Röntsch, Analytic results for color-singlet production at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J. C 79, 386 (2019).
  63. A. Behring, W. Bizoń, F. Caola, K. Melnikov, and R. Röntsch, Bottom quark mass effects in associated WH production with the H→bb¯ decay through NNLO QCD, Phys. Rev. D 101, 114012 (2020).
  64. M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
  65. R. Gauld, A. Gehrmann-De Ridder, E. Glover, A. Huss, and I. Majer, Precise predictions for WH+jet production at the LHC, Phys. Lett. B 817, 136335 (2021).
  66. R. Gauld, A. Gehrmann-De Ridder, E. W. N. Glover, A. Huss, and I. Majer, Vh+jet production in hadron-hadron collisions up to order αs3 in perturbative QCD, J. High Energy Phys. 03 (2022) 008.
  67. R. V. Harlander, S. Y. Klein, and M. Lipp, feyngame, Comput. Phys. Commun. 256, 107465 (2020).
  68. R. Harlander, S. Y. Klein, and M. C. Schaaf, feyngame-2.1—Feynman diagrams made easy, Proc. Sci. EPS-HEP2023 (2024) 657 [arXiv:2401.12778].
  69. L. Bündgen, R. V. Harlander, S. Y. Klein, and M. C. Schaaf, feyngame 3.0, Comput. Phys. Commun. 314, 109662 (2025).
  70. T. Becher and M. Neubert, On the structure of infrared singularities of gauge-theory amplitudes, J. High Energy Phys. 06 (2009) 081; 11 (2013) 24.
  71. T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102, 162001 (2009); 111, 199905(E) (2013).

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Phys. Rev. D 112, 034033– Published 27 August, 2025
  • Received 6 March 2025
  • Accepted 31 July 2025
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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.

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