- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Theoretical and experimental constraints in the μ−τ four-lepton sector of the SMEFT: Implications to neutrino self-interactions

Aadarsh Singh1, Giancarlo D’Ambrosio2,1, and Sudhir K. Vempati1

PDF

Phys. Rev. D 114, 035038 – Published 27 August, 2026

DOI: https://doi.org/10.1103/8z45-8cw5

Abstract

We study the dimension-six SMEFT four-lepton operators in the μ–τ sector. These operators control both charged-lepton scattering and neutrino self-interactions, the latter being weakly constrained by direct laboratory probes despite their importance for cosmological tensions. We compare three classes of constraints on the Warsaw-basis coefficients [Cℓℓ]2222, [Cℓℓ]2233, and [Cℓℓ]2332. We use perturbative unitarity from 2→2 partial-wave analysis, spin-summing positivity sum rules, and the experimental bounds from NA64μ and the global fit [Adam Falkowski et al., Compilation of low-energy constraints on 4-fermion operators in the SMEFT, J. High Energy Phys. 08 (2017) 123.]. We find that the global fit dominates for [Cℓℓ]2222 and [Cℓℓ]2332, while NA64μ provides the leading bound on [Cℓℓ]2233, with the unitarity line for this direction entering the range of collider energies near 200 GeV. Renormalization-group running between 1 GeV and 30 TeV modifies these coefficients by up to 10%. Translating these bounds onto the effective four-neutrino coupling Geff, we find values many orders of magnitude smaller than the strongly interacting regime motivated by the Hubble tension; this excludes heavy-mediator UV completions of strong νμ–νμ and νμ–ντ self-interactions within the validity of the dimension-six SMEFT and in the absence of tuned cancellations between operators, while leaving the cosmologically motivated light-mediator scenarios unconstrained by this analysis. Finally, we comment on the bounds these coefficients place on a leptophilic Lμ−Lτ Z′ UV completion. Our SMEFT-based current and projected NA64μ bounds reproduce the dedicated Z′ analyses already available in the literature. We also present a complementary analysis for the e–μ sector using projected JUNO sensitivities.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (88)

  1. Christina D. Kreisch, Francis-Yan Cyr-Racine, and Olivier Doré, Neutrino puzzle: Anomalies, interactions, and cosmological tensions, Phys. Rev. D 101, 123505 (2020).
  2. N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  3. Adam G. Riess et al., A comprehensive measurement of the local value of the Hubble constant with 1  km/s/Mpc uncertainty from the Hubble Space Telescope and the SH0ES team, Astrophys. J. Lett. 934, L7 (2022).
  4. Thejs Brinckmann, Jae Hyeok Chang, and Marilena LoVerde, Self-interacting neutrinos, the Hubble parameter tension, and the cosmic microwave background, Phys. Rev. D 104, 063523 (2021).
  5. Nikita Blinov, Kevin J. Kelly, Gordan Krnjaic, and Samuel D. McDermott, Constraining the self-interacting neutrino interpretation of the Hubble tension, Phys. Rev. Lett. 123, 191102 (2019).
  6. Miguel Escudero, Dan Hooper, Gordan Krnjaic, and Mathias Pierre, Cosmology with a very light lμ−−−lτ gauge boson, J. High Energy Phys. 03 (2019) 071.
  7. Kun-Feng Lyu, Emmanuel Stamou, and Lian-Tao Wang, Self-interacting neutrinos: Solution to Hubble tension versus experimental constraints, Phys. Rev. D 103, 015004 (2021).
  8. Jeffrey M. Berryman et al., Neutrino self-interactions: A white paper, Phys. Dark Universe 42, 101267 (2023).
  9. Anirban Das, Self-interacting neutrinos as a solution to the Hubble tension? in The European Physical Society Conference on High Energy Physics (EPS-HEP2021) (2022), arXiv:2109.03263.
  10. Shouvik Roy Choudhury, Steen Hannestad, and Thomas Tram, Updated constraints on massive neutrino self-interactions from cosmology in light of the H0 tension, J. Cosmol. Astropart. Phys. 03 (2021) 084.
  11. Steven Weinberg, Phenomenological Lagrangians, Physica A (Amsterdam) 96, 327 (1979).
  12. W. Buchmuller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B268, 621 (1986).
  13. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, J. High Energy Phys. 10 (2010) 085.
  14. Ilaria Brivio and Michael Trott, The standard model as an effective field theory, Phys. Rep. 793, 1 (2019).
  15. Athanasios 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.
  16. Adam Falkowski, Martin Gonzalez-Alonso, and Kin Mimouni, Compilation of low-energy constraints on 4-fermion operators in the SMEFT, J. High Energy Phys. 08 (2017) 123.
  17. Adam Falkowski, Martín González-Alonso, and Zahra Tabrizi, Reactor neutrino oscillations as constraints on effective field theory, J. High Energy Phys. 05 (2019) 173.
  18. John Ellis, Maeve Madigan, Ken Mimasu, Veronica Sanz, and Tevong You, Top, Higgs diboson and electroweak fit to the Standard Model effective field theory, J. High Energy Phys. 04 (2021) 279.
  19. Jacob J. Ethier, Giacomo Magni, Fabio Maltoni, Luca Mantani, Emanuele R. Nocera, Juan Rojo, Emma Slade, Eleni Vryonidou, and Cen Zhang, Combined SMEFT interpretation of Higgs diboson, and top quark data from the LHC, J. High Energy Phys. 11 (2021) 089.
  20. Laure Berthier and Michael Trott, Consistent constraints on the Standard Model effective field theory, J. High Energy Phys. 02 (2016) 069.
  21. R. L. Workman et al., Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  22. Andreas Crivellin and Bruce Mellado, Anomalies in particle physics and their implications for physics beyond the Standard Model, Nat. Rev. Phys. 6, 294 (2024).
  23. Wolfgang Altmannshofer, Stefania Gori, Maxim Pospelov, and Itay Yavin, Neutrino trident production: A powerful probe of new physics with neutrino beams, Phys. Rev. Lett. 113, 091801 (2014).
  24. W. Altmannshofer, S. Gori, M. Pospelov, and I. Yavin, Quark flavor transitions in lμ−−−lτ models, Phys. Rev. D 89, 095033 (2014).
  25. S. R. Mishra et al., Neutrino tridents and WZ interference, Phys. Rev. Lett. 66, 3117 (1991).
  26. S. Schael et al., Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP, Phys. Rep. 532, 119 (2013).
  27. Aielet Efrati, Adam Falkowski, and Yotam Soreq, Electroweak constraints on flavorful effective theories, J. High Energy Phys. 07 (2015) 018.
  28. Tyler Corbett, O. J. P. Eboli, J. Gonzalez-Fraile, and M. C. Gonzalez-Garcia, Constraining anomalous Higgs interaction, Phys. Rev. D 86, 075013 (2012).
  29. Jorge de Blas, Yong Du, Christophe Grojean, Jiayin Gu, Víctor Miralles, Michael E. Peskin, Junping Tian, Marcel Vos, and Eleni Vryonidou, Global SMEFT fits at future colliders, arXiv:2206.08326.
  30. A. Abada et al., FCC-ee: The lepton collider: Future circular collider conceptual design report volume 2, Eur. Phys. J. Special Topics 228, 261 (2019).
  31. CEPC Study Group, CEPC conceptual design report: Volume 2-physics & detector, arXiv:1811.10545.
  32. Philip Bambade et al., The International Linear Collider: A global project, arXiv:1903.01629.
  33. T. K. Charles et al., The Compact Linear Collider (CLIC)—2018 summary report, CERN Yellow Rep. Monogr. 2, 1 (2018).
  34. Yu. M. Andreev, Dipanwita Banerjee, Benjamin Banto Oberhauser, Johannes Bernhard, P. Bisio, Nikolaos Charitonidis, Paolo Crivelli, Emilio Depero, Alexander V. Dermenev, Sergey V. Donskov et al., First results in the search for dark sectors at NA64 with the CERN SPS high energy muon beam, Phys. Rev. Lett. 132, 211803 (2024).
  35. Paolo Crivelli, Josu Hernandez-Garcia, Jacobo Lopez-Pavon, Victor Martin Lozano, and Laura Molina Bueno, First bounds on effective muon interactions using the NA64μ experiment at CERN J. High Energy Phys. 07 (2026) 031.
  36. Carlotta Accettura et al., Towards a muon collider, Eur. Phys. J. C 83, 864 (2023).
  37. Hind Al Ali et al., The muon Smasher’s guide, Rep. Prog. Phys. 85, 084201 (2022).
  38. K. M. Black et al., Muon collider forum report, J. Instrum. 19, T02015 (2024).
  39. Tao Han, Yang Ma, and Keping Xie, Quark and gluon contents of a lepton at high energies, High Energy Phys. Nucl. Phys. 02 (2022) 154.
  40. Dario Buttazzo and Paride Paradisi, Probing the muon g−2 anomaly with the Higgs boson at a muon collider, Phys. Rev. D 104, 075021 (2021).
  41. T. Adam, F. An, G. An, Q. An, N. Anfimov, V. Antonelli, G. Baccolo, M. Baldoncini, E. Baussan, M. Bellato et al., JUNO conceptual design report, arXiv:1508.07166.
  42. Fengpeng An et al., Neutrino physics with JUNO, J. Phys. G Nucl. Part. Phys. 43, 030401 (2016).
  43. Angel Abusleme, Thomas Adam, Shakeel Ahmad, Sebastiano Aiello, Muhammad Akram, Nawab Ali, Fengpeng An, Guangpeng An, Qi An, Giuseppe Andronico et al., TAO conceptual design report: A precision measurement of the reactor antineutrino spectrum with sub-percent energy resolution, arXiv:2005.08745.
  44. Babak Abi, Roberto Acciarri, Mario A Acero, Giorge Adamov, David Adams, Marco Adinolfi, Zubayer Ahmad, Jhanzeb Ahmed, Tyler Alion, S Alonso Monsalve et al., Deep Underground Neutrino Experiment (DUNE) far detector technical design report, volume II: DUNE physics, 10.2172/1599307 (2020).
  45. Ke Abe, Ke Abe, H. Aihara, A. Aimi, R. Akutsu, C. Andreopoulos, I. Anghel, L. H. V. Anthony, M. Antonova, Y. Ashida et al., Hyper-Kamiokande design report, arXiv:1805.04163.
  46. M. G. Aartsen, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, I. Al Samarai, D. Altmann, K. Andeen, T. Anderson et al., Measurement of atmospheric neutrino oscillations at 6–56 GeV with IceCube DeepCore, Phys. Rev. Lett. 120, 071801 (2018).
  47. Silvia Adrian-Martinez, M. Ageron, F. Aharonian, S. Aiello, A. Albert, F. Ameli, E. Anassontzis, M. Andre, G. Androulakis, M. Anghinolfi et al., Letter of intent for KM3NeT 2.0, J. Phys. G Nucl. Part. Phys. 43, 084001 (2016).
  48. J. Leutgeb, J. Mager, and A. Rebhan, Determining the neutrino mass ordering and oscillation parameters with KM3NeT/ORCA, Eur. Phys. J. C 81, 1008 (2021).
  49. Yong Du, Hao-Lin Li, Jian Tang, Sampsa Vihonen, and Jiang-Hao Yu, Exploring SMEFT-induced nonstandard interactions: From COHERENT to neutrino oscillations, Phys. Rev. D 105, 075022 (2022).
  50. Qing-Hong Cao, Yandong Liu, and Shu-Run Yuan, Unitarity bounds and basis transformations in SMEFT: An analysis of Warsaw and SILH bases, Nucl. Phys. B1010, 116781 (2025).
  51. Grant N. Remmen and Nicholas L. Rodd, Flavor constraints from unitarity and analyticity, Phys. Rev. Lett. 125, 081601 (2020); 127, 149901(E) (2021).
  52. S. N. Gninenko, N. V. Krasnikov, and V. A. Matveev, Muon g−2 and searches for a new leptophobic sub-GeV dark boson in a missing-energy experiment at CERN, Phys. Rev. D 91, 095015 (2015).
  53. Luigi C Bresciani, Paride Paradisi, and Andrea Sainaghi, Unitarity bounds and sum rules in the SMEFT arXiv:2603.03423.
  54. Luigi C Bresciani, Gabriele Levati, and Paride Paradisi, Amplitudes and partial wave unitarity bounds, Phys. Rev. D 113, L071702 (2026).
  55. Luigi C Bresciani, Gabriele Levati, and Paride Paradisi, Positivity and partial wave unitarity bounds on ALP theories via amplitude methods, J. High Energy Phys. 07 (2026) 172.
  56. Grant N. Remmen and Nicholas L. Rodd, Consistency of the Standard Model effective field theory, J. High Energy Phys. 12 (2019) 032.
  57. Grant N. Remmen and Nicholas L. Rodd, Spinning sum rules for the dimension-six SMEFT, J. High Energy Phys. 09 (2022) 030.
  58. Carlos Duaso Pueyo, Harry Goodhew, Ciaran McCulloch, and Enrico Pajer, Perturbative unitarity bounds from momentum-space entanglement, J. High Energy Phys. 08 (2025) 001.
  59. Rafael Aoude and Camila S Machado, The rise of SMEFT on-shell amplitudes, J. High Energy Phys. 12 (2019) 058.
  60. Allan Adams, Nima Arkani-Hamed, Sergei Dubovsky, Alberto Nicolis, and Riccardo Rattazzi, Causality, analyticity and an IR obstruction to UV completion, J. High Energy Phys. 10 (2006) 014.
  61. Claudia de Rham, Scott Melville, Andrew J. Tolley, and Shuang-Yong Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96, 081702 (2017).
  62. Brando Bellazzini, Luca Martucci, and Riccardo Torre, Symmetries, sum rules and constraints on effective field theories, J. High Energy Phys. 09 (2014) 100.
  63. Ian Low, Riccardo Rattazzi, and Alessandro Vichi, Theoretical constraints on the Higgs effective couplings, J. High Energy Phys. 04 (2010) 126.
  64. Jacques Distler, Benjamin Grinstein, Rafael A. Porto, and Ira Z. Rothstein, Falsifying models of new physics via WW scattering, Phys. Rev. Lett. 98, 041601 (2007).
  65. Mikael Chala and Jose Santiago, Positivity bounds in the Standard Model effective field theory beyond tree level, Phys. Rev. D 105, L111901 (2022).
  66. Cen Zhang and Shuang-Yong Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev. D 100, 095003 (2019).
  67. Benjamin W. Lee, C. Quigg, and H. B. Thacker, Weak interactions at very high-energies: The role of the Higgs boson mass, Phys. Rev. D 16, 1519 (1977).
  68. Tyler Corbett, O. J. P. Eboli, and M. C. Gonzalez-Garcia, Unitarity constrains on dimension-six operators, Phys. Rev. D 91, 035014 (2015).
  69. X. G. He, G. C. Joshi, H. Lew, and R. R. Volkas, Simplest Z′ model, Phys. Rev. D 44, 2118 (1991).
  70. R. Foot, X. G. He, H. Lew, and R. R. Volkas, Model for a light Z′ boson, Phys. Rev. D 50, 4571 (1994).
  71. Andrzej J Buras, Andreas Crivellin, Fiona Kirk, Claudio Andrea Manzari, and Marc Montull, Global analysis of leptophilic Z′ bosons, J. High Energy Phys. 06 (2021) 001.
  72. Rebeca Gonzalez Suarez, Baibhab Pattnaik, and José Zurita, Leptophilic Z′ bosons at the FCC-ee: Discovery opportunities, Phys. Rev. D 111, 035029 (2025).
  73. Martin Bauer, Patrick Foldenauer, and Joerg Jaeckel, Hunting all the hidden photons, J. High Energy Phys. 07 (2018) 001.
  74. M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (N.Y.) 7, 404 (1959).
  75. C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
  76. Marcel Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev. 123, 1053 (1961).
  77. Andre Martin, Unitarity and high-energy behavior of scattering amplitudes, Phys. Rev. 129, 1432 (1963).
  78. Elizabeth E. Jenkins, Aneesh V. Manohar, and Michael Trott, Renormalization group evolution of the Standard Model dimension six operators I: Formalism and λ dependence, J. High Energy Phys. 10 (2013) 087.
  79. Elizabeth E. Jenkins, Aneesh V. Manohar, and Michael Trott, Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence, J. High Energy Phys. 01 (2014) 035.
  80. Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar, and Michael Trott, Renormalization group evolution of the Standard Model dimension six operators III: Gauge coupling dependence and phenomenology, J. High Energy Phys. 04 (2014) 159.
  81. Elizabeth E. Jenkins, Aneesh V. Manohar, and Peter Stoffer, Low-energy effective field theory below the electroweak scale: Operators and matching, J. High Energy Phys. 03 (2018) 016.
  82. Elizabeth E. Jenkins, Aneesh V. Manohar, and Peter Stoffer, Low-energy effective field theory below the electroweak scale: Anomalous dimensions, J. High Energy Phys. 01 (2018) 084.
  83. Jason Aebischer, Jacky Kumar, and David M. Straub, wilson: A python package for the running and matching of wilson coefficients above and below the electroweak scale, Eur. Phys. J. C 78, 1026 (2018).
  84. J. de Blas et al., Higgs boson studies at future particle colliders, J. High Energy Phys. 01 (2020) 139.
  85. Jorge Terol-Calvo, Mariam Tórtola, and Avelino Vicente, High-energy constraints from low-energy neutrino nonstandard interactions, Phys. Rev. D 101, 095010 (2020).
  86. Kevin J Kelly, Manibrata Sen, Walter Tangarife, and Yue Zhang, Origin of sterile neutrino dark matter via secret neutrino interactions with vector bosons, Phys. Rev. D 101, 115031 (2020).
  87. Carlos A. Argüelles, Ali Kheirandish, and Aaron C. Vincent, Imaging galactic dark matter with high-energy cosmic neutrinos, Phys. Rev. Lett. 119, 201801 (2017).
  88. Ranjini Mondol, Subhadip Bouri, Akash Kumar Saha, and Ranjan Laha, Road through darkness: Probing dark matter–neutrino interactions using KM3-230213A, arXiv:2506.19910.

Outline

Information

Phys. Rev. D 114, 035038– Published 27 August, 2026
  • Received 30 April 2026
  • Accepted 24 July 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