- Open Access
SMEFT effects on spin correlations and entanglement at NLO QCD in diboson production at hadron colliders
Phys. Rev. D 113, 093005 – Published 28 May, 2026
DOI: https://doi.org/10.1103/mr8r-bvcd
Abstract
We perform for the first time a full study of spin correlations in inclusive production of WZ boson pairs at the LHC with leptonic decays in the presence of next-to-leading-order QCD corrections and of effects from a dimension-six operator in the Standard-Model effective field theory (SMEFT) modifying the electroweak triple-gauge coupling. We carry out the complete quantum-state tomography of the diboson system and relate its results to common purity and spin-entanglement markers, highlighting the sizeable impact of both QCD corrections and SMEFT insertions. Additionally, we show how a naïve truncation at dimension six in the SMEFT expansion of the spin-density matrix can lead to a cumbersome spin interpretation of the quantum-tomography results.
Physics Subject Headings (PhySH)
Article Text
References (86)
- A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Quantum entanglement and Bell inequality violation at colliders, Prog. Part. Nucl. Phys. 139, 104134 (2024).
- Y. Afik et al., Quantum information meets high-energy physics: Input to the update of the European strategy for particle physics, Eur. Phys. J. Plus 140, 855 (2025).
- G. Aad et al. (ATLAS Collaboration), Observation of quantum entanglement with top quarks at the ATLAS detector, Nature (London) 633, 542 (2024).
- A. Hayrapetyan et al. (CMS Collaboration), Observation of quantum entanglement in top quark pair production in proton–proton collisions at , Rep. Prog. Phys. 87, 117801 (2024).
- A. Hayrapetyan et al. (CMS Collaboration), Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using events from proton-proton collisions at , Phys. Rev. D 110, 112016 (2024).
- A. J. Barr, Testing Bell inequalities in Higgs boson decays, Phys. Lett. B 825, 136866 (2022).
- J. A. Aguilar-Saavedra, A. Bernal, J. A. Casas, and J. M. Moreno, Testing entanglement and Bell inequalities in , Phys. Rev. D 107, 016012 (2023).
- J. A. Aguilar-Saavedra, Laboratory-frame tests of quantum entanglement in , Phys. Rev. D 107, 076016 (2023).
- M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Stringent bounds on HWW and HZZ anomalous couplings with quantum tomography at the LHC, J. High Energy Phys. 09 (2023) 195.
- A. Bernal, P. Caban, and J. Rembieliński, Entanglement and Bell inequalities violation in with anomalous coupling, Eur. Phys. J. C 83, 1050 (2023).
- F. Fabbri, J. Howarth, and T. Maurin, Isolating semi-leptonic decays for Bell inequality tests, Eur. Phys. J. C 84, 20 (2024).
- A. Bernal, P. Caban, and J. Rembieliński, Entanglement and Bell inequality violation in vector diboson systems produced in decays of spin-0 particles, Sci. Rep. 15, 23410 (2025).
- M. Sullivan, Constraining new physics with Tomography, arXiv:2410.10980.
- Y. Wu, R. Jiang, A. Ruzi, Y. Ban, X. Yan, and Q. Li, Testing Bell inequalities and probing quantum entanglement at CEPC, Phys. Rev. D 111, 036008 (2025).
- J. A. Aguilar-Saavedra, as a double-slit experiment, Phys. Lett. B 868, 139639 (2025).
- A. Subba, R. K. Singh, and R. M. Godbole, Looking into the quantum entanglement in at LHC within SMEFT framework, arXiv:2411.19171.
- M. Del Gratta, F. Fabbri, P. Lamba, F. Maltoni, and D. Pagani, Quantum properties of : Precise predictions in the SM and sensitivity to new physics, J. High Energy Phys. 09 (2025) 013.
- J. A. Aguilar-Saavedra, Quantum tomography beyond the leading order, Eur. Phys. J. C 85, 969 (2025).
- D. Gonçalves, A. Kaladharan, and A. Navarro, Higher-order corrections to quantum observables in , J. High Energy Phys. 11 (2025) 158.
- J. A. Aguilar-Saavedra, Momentum entanglement at colliders: the case, arXiv:2512.02104.
- R. Rahaman and R. K. Singh, Breaking down the entire spectrum of spin correlations of a pair of particles involving fermions and gauge bosons, Nucl. Phys. B984, 115984 (2022).
- R. Ashby-Pickering, A. J. Barr, and A. Wierzchucka, Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of massive particles, J. High Energy Phys. 05 (2023) 020.
- M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Bell inequalities and quantum entanglement in weak gauge boson production at the LHC and future colliders, Eur. Phys. J. C 83, 823 (2023).
- R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Probing new physics through entanglement in Diboson production, J. High Energy Phys. 12 (2023) 017.
- R. A. Morales, Exploring Bell inequalities and quantum entanglement in vector boson scattering, Eur. Phys. J. Plus 138, 1157 (2023).
- A. Subba and R. Rahaman, On bipartite and tripartite entanglement at present and future particle colliders, arXiv:2404.03292.
- M. Grossi, G. Pelliccioli, and A. Vicini, From angular coefficients to quantum observables: A phenomenological appraisal in di-boson systems, J. High Energy Phys. 12 (2024) 120.
- R. Grabarczyk, An improved Bell-CHSH observable for gauge boson pairs, arXiv:2410.18022.
- R. Ding et al., Quantum entanglement between gauge boson pairs at a Muon Collider, arXiv:2504.09832.
- D. Gonçalves, A. Kaladharan, F. Krauss, and A. Navarro, Quantum entanglement is quantum: ZZ production at the LHC, J. High Energy Phys. 12 (2025) 122.
- A. Ruzi, Y. Wu, R. Ding, and Q. Li, Searching quantum entanglement in the process, Chin. Phys. 50, 023103 (2026).
- M. Del Gratta, F. Fabbri, M. Grossi, F. Maltoni, D. Pagani, G. Pelliccioli, and A. Vicini, Z-boson quantum tomography at next-to-leading order, J. High Energy Phys. 02 (2026) 056.
- V. Durupt, F. Maltoni, and O. Mattelaer, Automated computation of spin-density matrices and quantum observables for collider physics, J. High Energy Phys. 04 (2026) 103.
- A. Subba and R. K. Singh, Probing anomalous couplings in the SMEFT with channel, arXiv:2512.06671.
- S. De, A. Dey, and T. Samui, Unfolding quantum entanglement from at a muon collider, arXiv:2512.09121.
- 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.
- A. Denner and G. Pelliccioli, NLO QCD predictions for doubly-polarized WZ production at the LHC, Phys. Lett. B 814, 136107 (2021).
- D. N. Le and J. Baglio, Doubly-polarized WZ hadronic cross sections at NLO accuracy, Eur. Phys. J. C 82, 917 (2022).
- G. Pelliccioli and R. Poncelet, Precise predictions for joint polarisation fractions in WZ production at the LHC, Phys. Rev. D 113, 053008 (2026).
- Z. Bern et al., Left-handed W bosons at the LHC, Phys. Rev. D 84, 034008 (2011).
- W. J. Stirling and E. Vryonidou, Electroweak gauge boson polarisation at the LHC, J. High Energy Phys. 07 (2012) 124.
- M. Aaboud et al. (ATLAS Collaboration), Measurement of production cross sections and gauge boson polarisation in collisions at with the ATLAS detector, Eur. Phys. J. C 79, 535 (2019).
- F. Boudjema and R. K. Singh, A Model independent spin analysis of fundamental particles using azimuthal asymmetries, J. High Energy Phys. 07 (2009) 028.
- S. Hill and W. K. Wootters, Entanglement of a pair of quantum bits, Phys. Rev. Lett. 78, 5022 (1997).
- F. Mintert and A. Buchleitner, An observable entanglement measure for unknown mixed quantum states, Phys. Rev. Lett. 98, 140505 (2008).
- C.-J. Zhang, Y.-X. Gong, Y.-S. Zhang, and G.-C. Guo, Observable estimation of entanglement for arbitrary finite-dimensional mixed states, Phys. Rev. A 78, 042308 (2008).
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
- A. Falkowski, M. Gonzalez-Alonso, A. Greljo, and D. Marzocca, Global constraints on anomalous triple gauge couplings in effective field theory approach, Phys. Rev. Lett. 116, 011801 (2016).
- A. Falkowski, M. Gonzalez-Alonso, A. Greljo, D. Marzocca, and M. Son, Anomalous triple gauge couplings in the effective field theory approach at the LHC, J. High Energy Phys. 02 (2017) 115.
- A. Azatov, R. Contino, C. S. Machado, and F. Riva, Helicity selection rules and noninterference for BSM amplitudes, Phys. Rev. D 95, 065014 (2017).
- A. Helset and M. Trott, On interference and non-interference in the SMEFT, J. High Energy Phys. 04 (2018) 038.
- A. Azatov, J. Elias-Miro, Y. Reyimuaji, and E. Venturini, Novel measurements of anomalous triple gauge couplings for the LHC, J. High Energy Phys. 10 (2017) 027.
- J. Baglio, S. Dawson, and I. M. Lewis, An NLO QCD effective field theory analysis of production at the LHC including fermionic operators, Phys. Rev. D 96, 073003 (2017).
- G. Panico, F. Riva, and A. Wulzer, Diboson interference resurrection, Phys. Lett. B 776, 473 (2018).
- M. Chiesa, A. Denner, and J.-N. Lang, Anomalous triple-gauge-boson interactions in vector-boson pair production with recola2, Eur. Phys. J. C 78, 467 (2018).
- J. Baglio, S. Dawson, and I. M. Lewis, NLO effects in EFT fits to production at the LHC, Phys. Rev. D 99, 035029 (2019).
- C. Grojean, M. Montull, and M. Riembau, Diboson at the LHC vs LEP, J. High Energy Phys. 03 (2019) 020.
- J. Baglio, S. Dawson, and S. Homiller, QCD corrections in Standard Model EFT fits to and production, Phys. Rev. D 100, 113010 (2019).
- A. Azatov, D. Barducci, and E. Venturini, Precision diboson measurements at hadron colliders, J. High Energy Phys. 04 (2019) 075.
- 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).
- C. Degrande and M. Maltoni, EFT observable stability under NLO corrections through interference revival, Phys. Lett. B 856, 138970 (2024).
- H. El Faham, G. Pelliccioli, and E. Vryonidou, Triple-gauge couplings in LHC diboson production: A SMEFT view from every angle, J. High Energy Phys. 08 (2024) 087.
- S. Jahedi, J. Lahiri, and A. Subba, Optimal sensitivity of anomalous charged triple gauge couplings through W boson helicity at the colliders, J. High Energy Phys. 07 (2025) 280.
- H. El Faham, G. Ventura, and E. Vryonidou, Diboson production in the SMEFT at dimension-8, J. High Energy Phys. 04 (2026) 050.
- P. Lo Chiatto, Interference resurrection of the dipole through quantum tomography, Phys. Rev. D 112, 015017 (2025).
- M. M. Altakach, P. Lamba, F. Maltoni, and K. Sakurai, Quantum properties of heavy-fermion pairs at a lepton collider with polarised beams, arXiv:2601.09558.
- M. Chiesa, C. Oleari, and E. Re, NLO EW corrections to diboson production matched to parton shower, Eur. Phys. J. C 80, 849 (2020).
- G. Pelliccioli and G. Zanderighi, Polarised-boson pairs at the LHC with NLOPS accuracy, Eur. Phys. J. C 84, 16 (2024).
- P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, J. High Energy Phys. 11 (2004) 040.
- S. Frixione, P. Nason, and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: The powheg method, J. High Energy Phys. 11 (2007) 070.
- S. Alioli, P. Nason, C. Oleari, and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the powheg box, J. High Energy Phys. 06 (2010) 043.
- T. Ježo and P. Nason, On the treatment of resonances in next-to-leading order calculations matched to a parton shower, J. High Energy Phys. 12 (2015) 065.
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- A. Denner, J.-N. Lang, and S. Uccirati, Recola2: REcursive computation of one-loop amplitudes 2, Comput. Phys. Commun. 224, 346 (2018).
- S. Frixione, Z. Kunszt, and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B467, 399 (1996).
- 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).
- R. D. Ball et al. (NNPDF Collaboration), Parton distributions from high-precision collider data, Eur. Phys. J. C 77, 663 (2017).
- G. Aad et al., Observation of gauge boson joint-polarisation states in production from collisions at with the ATLAS detector, Phys. Lett. B 843, 137895 (2023).
- 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).
- R. Aoude, A. J. Barr, F. Maltoni, and L. Satrioni, Decoherence effects in entangled fermion pairs at colliders, Phys. Rev. D 113, 076007 (2026).
- S.-J. Lin, M.-J. Liu, D. Y. Shao, and S.-Y. Wei, Spin correlations and Bell nonlocality in pair production from collisions with a thrust cut, J. High Energy Phys. 11 (2025) 082.
- J. Gu, S.-J. Lin, D. Y. Shao, L.-T. Wang, and S.-X. Yang, Decoherence in high energy collisions as renormalization group flow, arXiv:2510.13951.
- R. Bartocci, A. Biekötter, and T. Hurth, A global analysis of the SMEFT under the minimal MFV assumption, J. High Energy Phys. 05 (2024) 074.
- 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.
- J. de Blas, A. Goncalves, V. Miralles, L. Reina, L. Silvestrini, and M. Valli, Constraining new physics effective interactions via a global fit of electroweak, Drell-Yan, Higgs, top, and flavour observables, J. High Energy Phys. 03 (2026) 013.
- https://gitlab.com/POWHEG-BOX/RES/User-Processes/VV_pol.