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Precise predictions for joint polarization fractions in WZ production at the LHC

Giovanni Pelliccioli*

Rene Poncelet†

  • *Contact author: giovanni.pelliccioli@unimib.it
  • †Contact author: rene.poncelet@ifj.edu.pl
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Phys. Rev. D 113, 053008 – Published 25 March, 2026

DOI: https://doi.org/10.1103/m4j4-t34q

Abstract

We achieve for the first time NNLO QCD+NLO EW accuracy for doubly polarized WZ inclusive production at the LHC, in the case of fully leptonic decays. Additionally, we provide estimates for missing higher-order uncertainties in QCD associated with doubly polarized differential cross sections and joint polarization fractions, obtained both with standard scale variations and with a theory-nuisance-parameter approach. The study is carried out in the fiducial setup of a recent ATLAS analysis of Run-2 data.

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References (77)

  1. M. Aaboud et al. (ATLAS Collaboration), Measurement of W±Z production cross sections and gauge boson polarization in pp collisions at s=13  TeV with the ATLAS detector, Eur. Phys. J. C 79, 535 (2019).
  2. A. Tumasyan et al. (CMS Collaboration), Measurement of the inclusive and differential WZ production cross sections, polarization angles, and triple gauge couplings in pp collisions at s=13  TeV, J. High Energy Phys. 07 (2022) 032.
  3. G. Aad et al. (ATLAS Collaboration), Observation of gauge boson joint-polarisation states in W±Z production from pp collisions at s=13TeV with the ATLAS detector, Phys. Lett. B 843, 137895 (2023).
  4. G. Aad et al. (ATLAS Collaboration), Studies of the energy dependence of diboson polarization fractions and the radiation-amplitude-zero effect in WZ production with the ATLAS detector, Phys. Rev. Lett. 133, 101802 (2024); 133, 169901(E) (2024).
  5. A. Ballestrero, E. Maina, and G. Pelliccioli, W boson polarization in vector boson scattering at the LHC, J. High Energy Phys. 03 (2018) 170.
  6. D. Buarque Franzosi, O. Mattelaer, R. Ruiz, and S. Shil, Automated predictions from polarized matrix elements, J. High Energy Phys. 04 (2020) 082.
  7. A. Ballestrero, E. Maina, and G. Pelliccioli, Polarized vector boson scattering in the fully leptonic WZ and ZZ channels at the LHC, J. High Energy Phys. 09 (2019) 087.
  8. A. Ballestrero, E. Maina, and G. Pelliccioli, Different polarization definitions in same-sign WW scattering at the LHC, Phys. Lett. B 811, 135856 (2020).
  9. A. Denner and G. Pelliccioli, Polarized electroweak bosons in W+W− production at the LHC including NLO QCD effects, J. High Energy Phys. 09 (2020) 164.
  10. A. Denner and G. Pelliccioli, NLO QCD predictions for doubly-polarized WZ production at the LHC, Phys. Lett. B 814, 136107 (2021).
  11. R. Poncelet and A. Popescu, NNLO QCD study of polarised W+W− production at the LHC, J. High Energy Phys. 07 (2021) 023.
  12. A. Denner and G. Pelliccioli, NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC, J. High Energy Phys. 10 (2021) 097.
  13. D. N. Le and J. Baglio, Doubly-polarized WZ hadronic cross sections at NLO QCD+EW accuracy, Eur. Phys. J. C 82, 917 (2022).
  14. D. N. Le, J. Baglio, and T. N. Dao, Doubly-polarized WZ hadronic production at NLO QCD+EW: Calculation method and further results, Eur. Phys. J. C 82, 1103 (2022).
  15. M. Pellen, R. Poncelet, and A. Popescu, Polarised W+j production at the LHC: A study at NNLO QCD accuracy, J. High Energy Phys. 02 (2022) 160.
  16. M. Hoppe, M. Schönherr, and F. Siegert, Polarised cross sections for vector boson production with SHERPA, J. High Energy Phys. 04 (2024) 001.
  17. G. Pelliccioli and G. Zanderighi, Polarised-boson pairs at the LHC with NLOPS accuracy, Eur. Phys. J. C 84, 16 (2024).
  18. A. Denner, C. Haitz, and G. Pelliccioli, NLO EW corrections to polarised W+ W− production and decay at the LHC, Phys. Lett. B 850, 138539 (2024).
  19. T. N. Dao and D. N. Le, NLO electroweak corrections to doubly-polarized W+W− production at the LHC, Eur. Phys. J. C 84, 244 (2024).
  20. M. Javurkova, R. Ruiz, R. C. L. de Sá, and J. Sandesara, Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC, Phys. Lett. B 855, 138787 (2024).
  21. A. Denner, C. Haitz, and G. Pelliccioli, NLO EW and QCD corrections to polarised same-sign WW scattering at the LHC, J. High Energy Phys. 11 (2024) 115.
  22. T. N. Dao and D. N. Le, Polarized W+W− pairs at the LHC: Effects from bottom-quark induced processes at NLO QCD+EW, Eur. Phys. J. C 85, 108 (2025).
  23. C. Carrivale et al., Precise standard-model predictions for polarised Z-boson pair production and decay at the LHC, Eur. Phys. J. C 85, 1342 (2025).
  24. U. Haisch, J. Linder, G. Pelliccioli, E. Re, and G. Zanderighi, Polarized-boson pairs at NLO in the SMEFT, J. High Energy Phys. 11 (2025) 080.
  25. A. Denner, C. Haitz, and G. Pelliccioli, NLO QCD corrections to polarized diboson production in semileptonic final states, Phys. Rev. D 107, 053004 (2023).
  26. M. Grazzini, S. Kallweit, D. Rathlev, and M. Wiesemann, W±Z production at hadron colliders in NNLO QCD, Phys. Lett. B 761, 179 (2016).
  27. M. Grazzini, S. Kallweit, D. Rathlev, and M. Wiesemann, W±Z production at the LHC: Fiducial cross sections and distributions in NNLO QCD, J. High Energy Phys. 05 (2017) 139.
  28. B. Biedermann, A. Denner, and L. Hofer, Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC, J. High Energy Phys. 10 (2017) 043.
  29. M. Grazzini, S. Kallweit, J. M. Lindert, S. Pozzorini, and M. Wiesemann, NNLO QCD+NLO EW with Matrix+OpenLoops: Precise predictions for vector-boson pair production, J. High Energy Phys. 02 (2020) 087.
  30. M. Chiesa, C. Oleari, and E. Re, NLO QCD+NLO EW corrections to diboson production matched to parton shower, Eur. Phys. J. C 80, 849 (2020).
  31. J. M. Lindert, D. Lombardi, M. Wiesemann, G. Zanderighi, and S. Zanoli, W±Z production at NNLO QCD and NLO EW matched to parton showers with MiNNLOPS, J. High Energy Phys. 11 (2022) 036.
  32. F. J. Tackmann, Beyond scale variations: Perturbative theory uncertainties from nuisance parameters, J. High Energy Phys. 08 (2025) 098.
  33. J. McGowan, T. Cridge, L. A. Harland-Lang, and R. S. Thorne, Approximate N3LO parton distribution functions with theoretical uncertainties: MSHT20aN3LO PDFs, Eur. Phys. J. C 83, 185 (2023); 83, 302(E) (2023).
  34. M. A. Lim and R. Poncelet, Robust estimates of theoretical uncertainties at fixed-order in perturbation theory, Phys. Rev. D 112, L111901 (2025).
  35. 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.
  36. S. Chang, M. A. Luty, T. Ma, F. Montagno, and A. Wulzer, Quantifying EFT uncertainties in LHC searches, J. High Energy Phys. 01 (2026) 094.
  37. R. G. Stuart, General renormalization of the gauge invariant perturbation expansion near the Z0 resonance, Phys. Lett. B 272, 353 (1991).
  38. R. G. Stuart, Gauge invariance, analyticity and physical observables at the Z0 resonance, Phys. Lett. B 262, 113 (1991).
  39. A. Aeppli, F. Cuypers, and G. J. van Oldenborgh, O(Γ) corrections to W pair production in e+e− and γγ collisions, Phys. Lett. B 314, 413 (1993).
  40. A. Aeppli, G. J. van Oldenborgh, and D. Wyler, Unstable particles in one loop calculations, Nucl. Phys. B428, 126 (1994).
  41. A. Denner, S. Dittmaier, M. Roth, and L. Wieders, Electroweak corrections to charged-current e+e−→4fermion processes: Technical details and further results, Nucl. Phys. B724, 247 (2005); B854, 504(E) (2012).
  42. A. Denner and S. Dittmaier, Electroweak radiative corrections for collider physics, Phys. Rep. 864, 1 (2020).
  43. S. Actis, A. Denner, L. Hofer, A. Scharf, and S. Uccirati, Recursive generation of one-loop amplitudes in the standard model, J. High Energy Phys. 04 (2013) 037.
  44. S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf, and S. Uccirati, recola: Recursive computation of one-loop amplitudes, Comput. Phys. Commun. 214, 140 (2017).
  45. A. Denner, S. Dittmaier, and L. Hofer, collier: A fortran-based Complex one-loop library in extended regularizations, Comput. Phys. Commun. 212, 220 (2017).
  46. S. Catani and M. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B485, 291 (1997); B510, 503(E) (1998).
  47. S. Dittmaier, A general approach to photon radiation off fermions, Nucl. Phys. B565, 69 (2000).
  48. S. Catani, S. Dittmaier, M. H. Seymour, and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B627, 189 (2002).
  49. L. Basso, S. Dittmaier, A. Huss, and L. Oggero, Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay, Eur. Phys. J. C 76, 56 (2016).
  50. M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693, 259 (2010).
  51. M. Czakon and D. Heymes, Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys. B890, 152 (2014).
  52. 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.
  53. M. Pellen, R. Poncelet, A. Popescu, and T. Vitos, Angular coefficients in W+j production at the LHC with high precision, Eur. Phys. J. C 82, 693 (2022).
  54. M. Bury and A. van Hameren, Numerical evaluation of multi-gluon amplitudes for high energy factorization, Comput. Phys. Commun. 196, 592 (2015).
  55. F. Cascioli, P. Maierhofer, and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108, 111601 (2012).
  56. F. Buccioni, S. Pozzorini, and M. Zoller, On-the-fly reduction of open loops, Eur. Phys. J. C 78, 70 (2018).
  57. 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).
  58. T. Gehrmann, A. von Manteuffel, and L. Tancredi, The two-loop helicity amplitudes for qq¯′→V1V2→4 leptons, J. High Energy Phys. 09 (2015) 128.
  59. D. Bardin, A. Leike, T. Riemann, and M. Sachwitz, Energy-dependent width effects in e+e− annihilation near the Z-boson pole, Phys. Lett. B 206, 539 (1988).
  60. R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  61. A. Denner, S. Dittmaier, M. Roth, and D. Wackeroth, Electroweak radiative corrections to e+e−→WW→4 fermions in double-pole approximation: The RACOONWW approach, Nucl. Phys. B587, 67 (2000).
  62. R. D. Ball et al. (NNPDF Collaboration), Parton distributions from high-precision collider data, Eur. Phys. J. C 77, 663 (2017).
  63. V. Bertone, S. Carrazza, N. P. Hartland, and J. Rojo (NNPDF Collaboration), Illuminating the photon content of the proton within a global PDF analysis, SciPost Phys. 5, 008 (2018).
  64. 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).
  65. M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
  66. J. Ohnemus, An order αs calculation of hadronic W±Z production, Phys. Rev. D 44, 3477 (1991).
  67. U. Baur, T. Han, and J. Ohnemus, Amplitude zeros in W±Z production, Phys. Rev. Lett. 72, 3941 (1994).
  68. J. M. Cornwall, D. N. Levin, and G. Tiktopoulos, Derivation of gauge invariance from high-energy unitarity bounds on the S matrix, Phys. Rev. D 10, 1145 (1974); 11, 972(E) (1975).
  69. C. E. Vayonakis, Born helicity amplitudes and cross-sections in non-Abelian gauge theories, Lett. Nuovo Cimento 17, 383 (1976).
  70. M. S. Chanowitz and M. K. Gaillard, The TeV physics of strongly interacting W’s and Z’s, Nucl. Phys. B261, 379 (1985).
  71. G. J. Gounaris, R. Kögerler, and H. Neufeld, Relationship between longitudinally polarized vector bosons and their unphysical scalar partners, Phys. Rev. D 34, 3257 (1986).
  72. M. Rubin, G. P. Salam, and S. Sapeta, Giant QCD K-factors beyond NLO, J. High Energy Phys. 09 (2010) 084.
  73. Z. Bern et al., Left-handed W bosons at the LHC, Phys. Rev. D 84, 034008 (2011).
  74. A. Denner and S. Pozzorini, One-loop leading logarithms in electroweak radiative corrections. I. Results, Eur. Phys. J. C 18, 461 (2001).
  75. See Supplemental Material at http://link.aps.org/supplemental/10.1103/m4j4-t34q for differential NNLO QCD+NLO EW distributions in further kinematic observables.
  76. https://dirac.ac.uk/.
  77. G. Pelliccioli and R. Poncelet, https://github.com/multibosons/pol-wz-raw-data.

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Phys. Rev. D 113, 053008– Published 25 March, 2026
  • Received 10 November 2025
  • Accepted 5 March 2026
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