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
  • Access by Xinjiang University

Constraining dimension-six SMEFT with higher-order predictions for pptW

Nikolaos Kidonakis and Kaan Şimşek

Phys. Rev. D 113, 095004 – Published 5 May, 2026

DOI: https://doi.org/10.1103/6gpr-knw7

Abstract

We study single-top production in association with a W boson at the Large Hadron Collider (LHC) as a probe of dimension-6 Standard Model effective field theory (SMEFT) at leading order, next-to-leading order, and approximate next-to-next-to-leading order accuracy in quantum chromodynamics (QCD). The process is sensitive to operators that modify the top-quark weak and chromomagnetic dipole interactions, and we perform three-parameter linear and quadratic SMEFT fits using doubly differential top-quark distributions in transverse momentum and rapidity for the Run II and Run III configurations at the LHC. We provide a detailed account of the uncertainties and quantify the impact of the different uncertainty components across bins and perturbative orders. We find that effective scales up to 2 TeV can be probed in nonmarginalized fits, while in marginalized fits the corresponding scales are around 0.5 and 1.5 TeV for linear and quadratic fits, respectively.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (123)

  1. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085.
  2. A. Pomarol and F. Riva, Towards the ultimate SM fit to close in on Higgs physics, J. High Energy Phys. 01 (2013) 151.
  3. A. Falkowski, Effective field theory approach to LHC Higgs data, Pramana 87, 39 (2016).
  4. C. W. Murphy, Dimension-8 operators in the standard model effective field theory, J. High Energy Phys. 10 (2020) 174.
  5. H.-L. Li, Z. Ren, J. Shu, M.-L. Xiao, J.-H. Yu, and Y.-H. Zheng, Complete set of dimension-eight operators in the standard model effective field theory, Phys. Rev. D 104, 015026 (2021).
  6. 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).
  7. B. Henning, X. Lu, T. Melia, and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys. 347, 363 (2016).
  8. 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) 019(E).
  9. L. Graf, B. Henning, X. Lu, T. Melia, and H. Murayama, 2, 12, 117, 1959, 45171, 1170086, …: A Hilbert series for the QCD chiral Lagrangian, J. High Energy Phys. 01 (2020) 142.
  10. L. Gráf, B. Henning, X. Lu, T. Melia, and H. Murayama, Hilbert series, the Higgs mechanism, and HEFT, J. High Energy Phys. 02 (2022) 064.
  11. 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.
  12. A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho, and L. Trifyllis, SmeftFR—Feynman rules generator for the standard model effective field theory, Comput. Phys. Commun. 247, 106931 (2020).
  13. A. Dedes, J. Rosiek, M. Ryczkowski, K. Suxho, and L. Trifyllis, SmeftFR v3—Feynman rules generator for the standard model effective field theory, Comput. Phys. Commun. 294, 108943 (2024).
  14. I. Brivio, Y. Jiang, and M. Trott, The smeftsim package, theory and tools, J. High Energy Phys. 12 (2017) 070.
  15. I. Brivio, smeftsim 3.0—a practical guide, J. High Energy Phys. 04 (2020) 073.
  16. M. J. Baker, J. Fuentes-Martín, G. Isidori, and M. König, High- pT signatures in vector–leptoquark models, Eur. Phys. J. C 79, 334 (2019).
  17. C. Zhang and S.-Y. Zhou, Convex geometry perspective on the (standard model) effective field theory space, Phys. Rev. Lett. 125, 201601 (2020).
  18. C. de Rham, S. Kundu, M. Reece, A. J. Tolley, and S.-Y. Zhou, Snowmass white paper: UV constraints on IR physics, in Snowmass 2021 (Proceedings of the U.S. Community Study on the Future of Particle Physics, Seattle, Washington, USA, 2022), .
  19. A. Biekötter, L. E. G. Maskos, and B. D. Pecjak, Threshold corrections in SMEFT, arXiv:2601.15901.
  20. I. Brivio and M. Trott, The standard model as an effective field theory, Phys. Rep. 793, 1 (2019).
  21. Z. Han and W. Skiba, Effective theory analysis of precision electroweak data, Phys. Rev. D 71, 075009 (2005).
  22. V. Cirigliano, M. Gonzalez-Alonso, and M. L. Graesser, Non-standard charged current interactions: beta decays versus the LHC, J. High Energy Phys. 02 (2012) 046.
  23. C.-Y. Chen, S. Dawson, and C. Zhang, Electroweak effective operators and Higgs physics, Phys. Rev. D 89, 015016 (2014).
  24. J. Ellis, V. Sanz, and T. You, Complete Higgs sector constraints on dimension-6 operators, J. High Energy Phys. 07 (2014) 036.
  25. J. D. Wells and Z. Zhang, Precision electroweak analysis after the Higgs boson discovery, Phys. Rev. D 90, 033006 (2014).
  26. C. Hartmann, W. Shepherd, and M. Trott, The Z decay width in the SMEFT: yt and λ corrections at one loop, J. High Energy Phys. 03 (2016) 060.
  27. V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Constraining the top-Higgs sector of the standard model effective field theory, Phys. Rev. D 94, 034031 (2016).
  28. A. Falkowski, M. González-Alonso, and K. Mimouni, Compilation of low-energy constraints on 4-fermion operators in the SMEFT, J. High Energy Phys. 08 (2017) 123.
  29. J. de Blas, M. Ciuchini, E. Franco, S. Mishima, M. Pierini, L. Reina, and L. Silvestrini, Electroweak precision observables and Higgs-boson signal strengths in the standard model and beyond: Present and future, J. High Energy Phys. 12 (2016) 135.
  30. N. P. Hartland, F. Maltoni, E. R. Nocera, J. Rojo, E. Slade, E. Vryonidou, and C. Zhang, A Monte Carlo global analysis of the standard model effective field theory: The top quark sector, J. High Energy Phys. 04 (2019) 100.
  31. A. Biekötter, T. Corbett, and T. Plehn, The gauge-Higgs legacy of the LHC run II, SciPost Phys. 6, 064 (2019).
  32. C. Grojean, M. Montull, and M. Riembau, Diboson at the LHC vs LEP, J. High Energy Phys. 03 (2018) 020.
  33. J. Baglio, S. Dawson, S. Homiller, S. D. Lane, and I. M. Lewis, Validity of standard model EFT studies of VH and VV production at NLO, Phys. Rev. D 101, 115004 (2020).
  34. R. Boughezal, F. Petriello, and D. Wiegand, Removing flat directions in standard model EFT fits: How polarized electron-ion collider data can complement the LHC, Phys. Rev. D 101, 116002 (2020).
  35. R. Boughezal, C.-Y. Chen, F. Petriello, and D. Wiegand, Four-lepton Z boson decay constraints on the standard model EFT, Phys. Rev. D 103, 055015 (2021).
  36. J. J. Ethier, R. Gomez-Ambrosio, G. Magni, and J. Rojo, SMEFT analysis of vector boson scattering and diboson data from the LHC run II, Eur. Phys. J. C 81, 560 (2021).
  37. S. Carrazza, C. Degrande, S. Iranipour, J. Rojo, and M. Ubiali, Can new physics hide inside the proton?, Phys. Rev. Lett. 123, 132001 (2019).
  38. J. Ellis, C. W. Murphy, V. Sanz, and T. You, Updated global SMEFT fit to Higgs, diboson and electroweak data, J. High Energy Phys. 06 (2018) 146.
  39. S. Dawson, P. P. Giardino, and A. Ismail, Standard model EFT and the Drell-Yan process at high energy, Phys. Rev. D 99, 035044 (2019).
  40. S. Alioli, R. Boughezal, E. Mereghetti, and F. Petriello, Novel angular dependence in Drell-Yan lepton production via dimension-8 operators, Phys. Lett. B 809, 135703 (2020).
  41. R. Boughezal, E. Mereghetti, and F. Petriello, Dilepton production in the SMEFT at O(1/Λ4), Phys. Rev. D 104, 095022 (2021).
  42. T. Cohen, X. Lu, and Z. Zhang, STrEAMlining EFT matching, SciPost Phys. 10, 098 (2021).
  43. X. Li, K. Mimasu, K. Yamashita, C. Yang, C. Zhang, and S.-Y. Zhou, Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics, J. High Energy Phys. 10 (2022) 107.
  44. S. Dawson, D. Fontes, S. Homiller, and M. Sullivan, Role of dimension-eight operators in an EFT for the 2HDM, Phys. Rev. D 106, 055012 (2022).
  45. A. Tumasyan et al. (CMS Collaboration), Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell-Yan production in proton-proton collisions at s=13TeV, Eur. Phys. J. C 83, 628 (2023).
  46. R. Grober, M. Muhlleitner, M. Spira, and J. Streicher, NLO QCD corrections to Higgs pair production including dimension-6 operators, J. High Energy Phys. 09 (2015) 092.
  47. C. Zhang, Single top production at next-to-leading order in the standard model effective field theory, Phys. Rev. Lett. 116, 162002 (2016).
  48. G. Passarino and M. Trott, The standard model effective field theory and next to leading order, arXiv:1610.08356.
  49. C. Englert, P. Galler, and C. D. White, Effective field theory and scalar extensions of the top quark sector, Phys. Rev. D 101, 035035 (2020).
  50. S. Dawson, M. Forslund, and P. P. Giardino, NLO SMEFT electroweak corrections to Higgs boson decays to four leptons in the narrow width approximation, Phys. Rev. D 111, 015016 (2025).
  51. L. Bellafronte, S. Dawson, C. Del Pio, M. Forslund, and P. P. Giardino, Complete NLO SMEFT electroweak corrections to Higgs decays, Phys. Rev. Lett. 136, 051801 (2026).
  52. L. Bellafronte, S. Dawson, C. Del Pio, M. Forslund, and P. P. Giardino, Higgs decays at NLO in the SMEFT, arXiv:2601.09599.
  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. C. Degrande, G. Durieux, F. Maltoni, K. Mimasu, E. Vryonidou, and C. Zhang, Automated one-loop computations in the standard model effective field theory, Phys. Rev. D 103, 096024 (2021).
  55. N. Kidonakis and A. Tonero, SMEFT chromomagnetic dipole operator contributions to tt¯ production at approximate NNLO in QCD, Eur. Phys. J. C 84, 591 (2024).
  56. G. Aad et al. (ATLAS Collaboration), Evidence for the associated production of a W boson and a top quark in ATLAS at s=7TeV, Phys. Lett. B 716, 142 (2012).
  57. S. Chatrchyan et al. (CMS Collaboration), Evidence for associated production of a single top quark and W boson in pp collisions at s=7TeV, Phys. Rev. Lett. 110, 022003 (2013).
  58. S. Chatrchyan et al. (CMS Collaboration), Observation of the associated production of a single top quark and a W boson in pp collisions at s=8TeV, Phys. Rev. Lett. 112, 231802 (2014).
  59. G. Aad et al. (ATLAS Collaboration), Measurement of the production cross-section of a single top quark in association with a W boson at 8 TeV with the ATLAS experiment, J. High Energy Phys. 01 (2015) 064.
  60. M. Aaboud et al. (ATLAS Collaboration), Measurement of the cross-section for producing a W boson in association with a single top quark in pp collisions at s=13TeV with ATLAS, J. High Energy Phys. 01 (2015) 063.
  61. M. Aaboud et al. (ATLAS Collaboration), Measurement of differential cross-sections of a single top quark produced in association with a W boson at s=13TeV with ATLAS, Eur. Phys. J. C 78, 186 (2018).
  62. A. M. Sirunyan et al. (CMS Collaboration), Measurement of the production cross section for single top quarks in association with W bosons in proton-proton collisions at s=13TeV, J. High Energy Phys. 10 (2018) 117.
  63. M. Aaboud et al. (ATLAS, CMS Collaborations), Combinations of single-top-quark production cross-section measurements and |fLVVtb| determinations at s=7 and 8 TeV with the ATLAS and CMS experiments, J. High Energy Phys. 05 (2019) 088.
  64. G. Aad et al. (ATLAS Collaboration), Measurement of single top-quark production in association with a W boson in the single-lepton channel at s=8TeV with the ATLAS detector, Eur. Phys. J. C 81, 720 (2021).
  65. A. Tumasyan et al. (CMS Collaboration), Observation of tW production in the single-lepton channel in pp collisions at s=13TeV, J. High Energy Phys. 11 (2021) 111.
  66. A. Tumasyan et al. (CMS Collaboration), Measurement of inclusive and differential cross sections for single top quark production in association with a W boson in proton-proton collisions at s=13TeV, J. High Energy Phys. 07 (2023) 046.
  67. G. Aad et al. (ATLAS Collaboration), Measurement of single top-quark production in association with a W boson in pp collisions at s=13TeV with the ATLAS detector, Phys. Rev. D 110, 072010 (2024).
  68. A. Hayrapetyan et al. (CMS Collaboration), Measurement of inclusive and differential cross sections of single top quark production in association with a W boson in proton-proton collisions at s=13.6TeV, J. High Energy Phys. 01 (2025) 107.
  69. G. A. Ladinsky and C. P. Yuan, The W—top background to heavy Higgs production, Phys. Rev. D 43, 789 (1991).
  70. A. Heinson, A. S. Belyaev, and E. E. Boos, Single top quarks at the fermilab tevatron, Phys. Rev. D 56, 3114 (1997).
  71. S. Moretti, Single top production in the t W+ channel and Higgs signals via HW+W at the Large Hadron Collider, Phys. Rev. D 56, 7427 (1997).
  72. A. S. Belyaev, E. E. Boos, and L. V. Dudko, Single top quark at future hadron colliders: Complete signal and background study, Phys. Rev. D 59, 075001 (1999).
  73. T. M. P. Tait, The tW mode of single top production, Phys. Rev. D 61, 034001 (1999).
  74. A. Belyaev and E. Boos, Single top quark tW+X production at the CERN LHC: A closer look, Phys. Rev. D 63, 034012 (2001).
  75. S. Zhu, Next-to-leading order QCD corrections to bgtW at CERN large hadron collider, Phys. Lett. B 524, 283 (2002); 537, 351(E) (2002).
  76. J. M. Campbell and F. Tramontano, Next-to-leading order corrections to Wt production and decay, Nucl. Phys. B726, 109 (2005).
  77. Q.-H. Cao, Demonstration of one cutoff phase space slicing method: Next-to-leading order QCD corrections to the tW associated production in hadron collision, arXiv:0801.1539.
  78. S. Frixione, E. Laenen, P. Motylinski, B. R. Webber, and C. D. White, Single-top hadroproduction in association with a W boson, J. High Energy Phys. 07 (2008) 029.
  79. E. Re, Single-top Wt-channel production matched with parton showers using the POWHEG method, Eur. Phys. J. C 71, 1547 (2011).
  80. L.-B. Chen and J. Wang, Analytic two-loop master integrals for tW production at hadron colliders: I *, Chin. Phys. C 45, 123106 (2021).
  81. M.-M. Long, R.-Y. Zhang, W.-G. Ma, Y. Jiang, L. Han, Z. Li, and S.-S. Wang, Two-loop master integrals for the single top production associated with W boson, arXiv:2111.14172.
  82. L.-B. Chen, L. Dong, H. T. Li, Z. Li, J. Wang, and Y. Wang, One-loop squared amplitudes for hadronic tW production at next-to-next-to-leading order in QCD, J. High Energy Phys. 08 (2022) 211.
  83. J. Wang and Y. Wang, Analytic two-loop master integrals for tW production at hadron colliders. Part II, J. High Energy Phys. 02 (2022) 127.
  84. L.-B. Chen, L. Dong, H. T. Li, Z. Li, J. Wang, and Y. Wang, Analytic two-loop QCD amplitudes for tW production: Leading color and light fermion-loop contributions, Phys. Rev. D 106, 096029 (2022).
  85. L.-B. Chen, L. Dong, H. T. Li, Z. Li, J. Wang, and Y. Wang, Complete two-loop QCD amplitudes for tW production at hadron colliders, J. High Energy Phys. 07 (2022) 089.
  86. N. Kidonakis, Single top production at the tevatron: Threshold resummation and finite-order soft gluon corrections, Phys. Rev. D 74, 114012 (2006).
  87. N. Kidonakis, Higher-order soft gluon corrections in single top quark production at the LHC, Phys. Rev. D 75, 071501 (2007).
  88. N. Kidonakis, Two-loop soft anomalous dimensions for single top quark associated production with a W or H, Phys. Rev. D 82, 054018 (2010).
  89. N. Kidonakis, NNLL threshold resummation for top-pair and single-top production, Phys. Part. Nucl. 45, 714 (2014).
  90. N. Kidonakis, Top quark production, in Helmholtz International Summer School on Physics of Heavy Quarks and Hadrons (2014), pp. 139–168, arXiv:1311.0283.
  91. N. Kidonakis, Single-top transverse-momentum distributions at approximate NNLO, Phys. Rev. D 93, 054022 (2016).
  92. N. Kidonakis, Soft-gluon corrections for tW production at N3LO, Phys. Rev. D 96, 034014 (2017).
  93. N. Kidonakis, Soft-gluon corrections in top-quark production, Int. J. Mod. Phys. A 33, 1830021 (2018).
  94. N. Kidonakis, Soft anomalous dimensions for single-top production at three loops, Phys. Rev. D 99, 074024 (2019).
  95. N. Kidonakis and N. Yamanaka, Higher-order corrections for tW production at high-energy hadron colliders, J. High Energy Phys. 05 (2021) 278.
  96. N. Kidonakis, NNLL resummation for s-channel single top quark production, Phys. Rev. D 81, 054028 (2010).
  97. N. Kidonakis, Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel single top quark production, Phys. Rev. D 83, 091503 (2011).
  98. N. Kidonakis, Top-quark transverse-momentum distributions in t-channel single-top production, Phys. Rev. D 88, 031504 (2013).
  99. N. Kidonakis, Resummation for s-channel single-top production, Nucl. Phys. B1024, 117352 (2026).
  100. C. S. Li, H. T. Li, D. Y. Shao, and J. Wang, Momentum-space threshold resummation in tW production at the LHC, J. High Energy Phys. 06 (2019) 125.
  101. J.-L. Ding, H. T. Li, and J. Wang, Next-to-next-to-leading order threshold soft function for tW production, J. High Energy Phys. 05 (2025) 143.
  102. J.-L. Ding, H. T. Li, and J. Wang, Approximate N2LO and N3LO QCD predictions for tW production, arXiv:2512.10711.
  103. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140, 418 (2001).
  104. V. Shtabovenko, R. Mertig, and F. Orellana, New developments in feyncalc9.0, Comput. Phys. Commun. 207, 432 (2016).
  105. V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020).
  106. V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc10: Do multiloop integrals dream of computer codes?, Comput. Phys. Commun. 306, 109357 (2025).
  107. R. Mertig, M. Bohm, and A. Denner, feyncalc: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64, 345 (1991).
  108. 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).
  109. G. P. Lepage, Adaptive multidimensional integration: VEGAS enhanced, J. Comput. Phys. 439, 110386 (2021).
  110. G. P. Lepage, gplepage/vegas: vegas version 6.1.2, Zenodo (2024), 10.5281/zenodo.11238512.
  111. P. Mastrolia, E. Mirabella, and T. Peraro, Integrand reduction of one-loop scattering amplitudes through Laurent series expansion, J. High Energy Phys. 06 (2012) 095; 11 (2012) 128(E).
  112. T. Peraro, Ninja: Automated integrand reduction via Laurent expansion for one-loop amplitudes, Comput. Phys. Commun. 185, 2771 (2014).
  113. V. Hirschi and T. Peraro, Tensor integrand reduction via Laurent expansion, J. High Energy Phys. 06 (2016) 060.
  114. A. Denner, S. Dittmaier, and L. Hofer, Collier: A Fortran-based complex one-loop LIbrary in extended regularizations, Comput. Phys. Commun. 212, 220 (2017).
  115. S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Martin, and R. S. Thorne, Parton distributions from LHC, HERA, tevatron and fixed target data: MSHT20 PDFs, Eur. Phys. J. C 81, 341 (2021).
  116. A. M. Sirunyan et al. (CMS Collaboration), Measurement of normalized differential tt¯ cross sections in the dilepton channel from pp collisions at s=13TeV, J. High Energy Phys. 04 (2018) 060.
  117. Search for, H±W±AW±μμ in pptt¯ events using an eμμ signature with the ATLAS detector at s=13TeV (2021).
  118. G. Aad et al. (ATLAS Collaboration), Luminosity determination in pp collisions at s=13TeV using the ATLAS detector at the LHC, Eur. Phys. J. C 83, 982 (2023).
  119. F. Cornet-Gomez, V. Miralles, M. Miralles López, M. Moreno Llácer, and M. Vos, Future collider constraints on top-quark operators, J. High Energy Phys. 10 (2025) 156.
  120. E. Celada, T. Giani, J. ter Hoeve, L. Mantani, J. Rojo, A. N. Rossia, M. O. A. Thomas, and E. Vryonidou, Mapping the SMEFT at high-energy colliders: From LEP and the (HL-)LHC to the FCC-ee, J. High Energy Phys. 09 (2024) 091.
  121. G. Aad et al. (ATLAS Collaboration), Inclusive and differential cross-sections for dilepton tt¯ production measured in s=13TeVpp collisions with the ATLAS detector, J. High Energy Phys. 07 (2023) 141.
  122. A. Tumasyan et al. (CMS Collaboration), Measurement of differential tt¯ production cross sections in the full kinematic range using lepton+jets events from proton-proton collisions at s=13TeV, Phys. Rev. D 104, 092013 (2021).
  123. N. Kidonakis and K. Şimşek, tW_project_data, https://github.com/kagsimsek/tW_project_data.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation