- 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

Enabling thermal dark matter within the vanilla Lμ−Lτ model

Nicolás Bernal1,*, Jacinto P. Neto2,3,4,†, Javier Silva-Malpartida5,‡, and Farinaldo S. Queiroz2,3,6,7,§

  • *Contact author: nicolas.bernal@nyu.edu
  • †Contact author: jacinto.neto.100@ufrn.edu.br
  • ‡Contact author: javier.silvam@pucp.edu.pe
  • §Contact author: farinaldo.queiroz@ufrn.br
PDF

Phys. Rev. D 112, 075042 – Published 22 October, 2025

DOI: https://doi.org/10.1103/8g85-c8sh

Abstract

Thermal dark matter is a compelling setup that has been probed by a multitude of experiments, mostly in the GeV–TeV mass range. The thermal paradigm in the sub-GeV range is about to experience the same experimental test with the next generation of low-energy accelerators and light dark matter detectors. Motivated by this, we investigate thermal dark matter in the Lμ−Lτ and assess how the introduction of a matter-dominated era impacts the parameter that yields the correct relic density. Interestingly, we show that the projected experiments, such as the Muon (Synchrotron) Ion Collider, Future Circular Collider-ee, and Light Dark Matter eXperiment, will probe a large region of the viable parameter space that yields the correct relic density. In the GeV–TeV mass regime, the usual large-scale detectors push the sensitivity. Our work highlights the rich interplay between early-Universe dynamics, dark matter phenomenology, and the discovery potential of next-generation experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (144)

  1. E. Aprile et al. (XENON Collaboration), First dark matter search with nuclear recoils from the XENONnT experiment, Phys. Rev. Lett. 131, 041003 (2023).
  2. J. Aalbers et al. (LZ Collaboration), Dark matter search results from 4.2 Tonne-years of exposure of the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 135, 011802 (2025).
  3. X. G. He, G. C. Joshi, H. Lew, and R. R. Volkas, New Z′ phenomenology, Phys. Rev. D 43, 22 (1991).
  4. X.-G. He, G. C. Joshi, H. Lew, and R. R. Volkas, Simplest Z′ model, Phys. Rev. D 44, 2118 (1991).
  5. S. Baek and P. Ko, Phenomenology of U(1)(Lμ−Lτ) charged dark matter at PAMELA and colliders, J. Cosmol. Astropart. Phys. 10 (2009) 011.
  6. J. Heeck and W. Rodejohann, Gauged Lμ−Lτ symmetry at the electroweak scale, Phys. Rev. D 84, 075007 (2011).
  7. W. Altmannshofer, S. Gori, M. Pospelov, and I. Yavin, Quark flavor transitions in Lμ−Lτ models, Phys. Rev. D 89, 095033 (2014).
  8. W. Altmannshofer and I. Yavin, Predictions for lepton flavor universality violation in rare B decays in models with gauged Lμ−Lτ, Phys. Rev. D 92, 075022 (2015).
  9. A. Crivellin, G. D’Ambrosio, and J. Heeck, Explaining h→μ±τ∓, B→K*μ+μ− and B→Kμ+μ−/B→Ke+e− in a two-Higgs-doublet model with gauged Lμ−Lτ, Phys. Rev. Lett. 114, 151801 (2015).
  10. S. Baek, Dark matter and muon (g−2) in local U(1)Lμ−Lτ-extended Ma Model, Phys. Lett. B 756, 1 (2016).
  11. F. Elahi and A. Martin, Constraints on Lμ−Lτ interactions at the LHC and beyond, Phys. Rev. D 93, 015022 (2016).
  12. A. Biswas, S. Choubey, and S. Khan, Neutrino mass, dark matter and anomalous magnetic moment of muon in a U(1)Lμ−Lτ model, J. High Energy Phys. 09 (2016) 147.
  13. S. Patra, S. Rao, N. Sahoo, and N. Sahu, Gauged U(1)Lμ−Lτ model in light of muon g−2 anomaly, neutrino mass and dark matter phenomenology, Nucl. Phys. B917, 317 (2017).
  14. I. Holst, D. Hooper, and G. Krnjaic, Simplest and most predictive model of Muon g-2 and thermal dark matter, Phys. Rev. Lett. 128, 141802 (2022).
  15. G.-y. Huang, S. Jana, F. S. Queiroz, and W. Rodejohann, Probing the RK(*) anomaly at a muon collider, Phys. Rev. D 105, 015013 (2022).
  16. Y. M. Andreev et al. (NA64 Collaboration), First results in the search for dark sectors at NA64 with the CERN SPS high energy Muon beam, Phys. Rev. Lett. 132, 211803 (2024).
  17. A. Boccaletti et al., High precision calculation of the hadronic vacuum polarisation contribution to the muon anomaly, arXiv:2407.10913.
  18. C. Davies, Muon g-2, Proc. Sci. LATTICE2024 (2025) 019 [arXiv:2503.03364].
  19. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, Phys. Rep. 1143, 1 (2025).
  20. D. P. Aguillard et al. (Muon g-2 Collaboration), Measurement of the positive muon anomalous magnetic moment to 127 ppb, Phys. Rev. Lett. 135, 101802 (2025); arXiv:2506.03069.
  21. M. Escudero, D. Hooper, G. Krnjaic, and M. Pierre, Cosmology with a very light Lμ–Lτ gauge boson, J. High Energy Phys. 03 (2019) 071.
  22. C.-H. Chen and C.-W. Chiang, Flavor anomalies in leptoquark model with gauged U(1)Lμ−Lτ, Phys. Rev. D 109, 075004 (2024).
  23. Z.-W. Wang, Z.-L. Han, F. Huang, Y. Jin, and H. Li, Prospects of Z’ portal dark matter in U(1)Lμ−Lτ, Phys. Rev. D 111, 095017 (2025).
  24. G. F. Giudice, E. W. Kolb, and A. Riotto, Largest temperature of the radiation era and its cosmological implications, Phys. Rev. D 64, 023508 (2001).
  25. N. Fornengo, A. Riotto, and S. Scopel, Supersymmetric dark matter and the reheating temperature of the universe, Phys. Rev. D 67, 023514 (2003).
  26. C. Pallis, Massive particle decay and cold dark matter abundance, Astropart. Phys. 21, 689 (2004).
  27. G. B. Gelmini and P. Gondolo, Neutralino with the right cold dark matter abundance in (almost) any supersymmetric model, Phys. Rev. D 74, 023510 (2006).
  28. M. Drees, H. Iminniyaz, and M. Kakizaki, Abundance of cosmological relics in low-temperature scenarios, Phys. Rev. D 73, 123502 (2006).
  29. C. E. Yaguna, An intermediate framework between WIMP, FIMP, and EWIP dark matter, J. Cosmol. Astropart. Phys. 02 (2012) 006.
  30. L. Roszkowski, S. Trojanowski, and K. Turzyński, Neutralino and gravitino dark matter with low reheating temperature, J. High Energy Phys. 11 (2014) 146.
  31. M. Drees and F. Hajkarim, Dark matter production in an early matter dominated era, J. Cosmol. Astropart. Phys. 02 (2018) 057.
  32. N. Bernal, C. Cosme, and T. Tenkanen, Phenomenology of self-interacting dark matter in a matter-dominated universe, Eur. Phys. J. C 79, 99 (2019).
  33. N. Bernal, C. Cosme, T. Tenkanen, and V. Vaskonen, Scalar singlet dark matter in non-standard cosmologies, Eur. Phys. J. C 79, 30 (2019).
  34. C. Cosme, M. Dutra, T. Ma, Y. Wu, and L. Yang, Neutrino portal to FIMP dark matter with an early matter era, J. High Energy Phys. 03 (2021) 026.
  35. G. Arcadi, J. P. Neto, F. S. Queiroz, and C. Siqueira, Roads for right-handed neutrino dark matter: Fast expansion, standard freeze-out, and early matter domination, Phys. Rev. D 105, 035016 (2022).
  36. P. Arias, N. Bernal, D. Karamitros, C. Maldonado, L. Roszkowski, and M. Venegas, New opportunities for axion dark matter searches in nonstandard cosmological models, J. Cosmol. Astropart. Phys. 11 (2021) 003.
  37. P. Asadi, T. R. Slatyer, and J. Smirnov, WIMPs without weakness: Generalized mass window with entropy injection, Phys. Rev. D 106, 015012 (2022).
  38. N. Bernal and Y. Xu, WIMPs during reheating, J. Cosmol. Astropart. Phys. 12 (2022) 017.
  39. P. N. Bhattiprolu, G. Elor, R. McGehee, and A. Pierce, Freezing-in hadrophilic dark matter at low reheating temperatures, J. High Energy Phys. 01 (2023) 128.
  40. D. Chowdhury and A. Hait, Thermalization in the presence of a time-dependent dissipation and its impact on dark matter production, J. High Energy Phys. 09 (2023) 085.
  41. M. R. Haque, D. Maity, and R. Mondal, WIMPs, FIMPs, and inflaton phenomenology via reheating, CMB and ΔNeff, J. High Energy Phys. 09 (2023) 012.
  42. D. K. Ghosh, A. Ghoshal, and S. Jeesun, Axion-like particle (ALP) portal freeze-in dark matter confronting ALP search experiments, J. High Energy Phys. 01 (2024) 026.
  43. J. Silva-Malpartida, N. Bernal, J. Jones-Pérez, and R. A. Lineros, From WIMPs to FIMPs with low reheating temperatures, J. Cosmol. Astropart. Phys. 09 (2023) 015.
  44. B. Barman, N. Bernal, and Y. Xu, Resonant reheating, J. Cosmol. Astropart. Phys. 08 (2024) 014.
  45. J. Silva-Malpartida, N. Bernal, J. Jones-Pérez, and R. A. Lineros, From WIMPs to FIMPs: Impact of early matter domination, J. Cosmol. Astropart. Phys. 03 (2025) 003.
  46. N. Bernal, C. S. Fong, and Ó. Zapata, Probing low-reheating scenarios with minimal freeze-in dark matter, J. High Energy Phys. 02 (2025) 161.
  47. G. Bélanger, N. Bernal, and A. Pukhov, Z’-mediated dark matter with low-temperature reheating, J. High Energy Phys. 03 (2025) 079.
  48. A. Banerjee, D. Chowdhury, A. Hait, and M. S. Islam, Dark matter cooling during early matter-domination boosts sub-earth halos, J. Cosmol. Astropart. Phys. 03 (2025) 030.
  49. N. Bernal, E. Cervantes, K. Deka, and A. Hryczuk, Freezing-in cannibals with low-reheating temperature, J. High Energy Phys. 09 (2025) 083.
  50. A. M. Green, Supersymmetry and primordial black hole abundance constraints, Phys. Rev. D 60, 063516 (1999).
  51. M. Y. Khlopov, A. Barrau, and J. Grain, Gravitino production by primordial black hole evaporation and constraints on the inhomogeneity of the early universe, Classical Quantum Gravity 23, 1875 (2006).
  52. D.-C. Dai, K. Freese, and D. Stojkovic, Constraints on dark matter particles charged under a hidden gauge group from primordial black holes, J. Cosmol. Astropart. Phys. 06 (2009) 023.
  53. T. Fujita, M. Kawasaki, K. Harigaya, and R. Matsuda, Baryon asymmetry, dark matter, and density perturbation from primordial black holes, Phys. Rev. D 89, 103501 (2014).
  54. R. Allahverdi, J. Dent, and J. Osiński, Nonthermal production of dark matter from primordial black holes, Phys. Rev. D 97, 055013 (2018).
  55. O. Lennon, J. March-Russell, R. Petrossian-Byrne, and H. Tillim, Black hole genesis of dark matter, J. Cosmol. Astropart. Phys. 04 (2018) 009.
  56. L. Morrison, S. Profumo, and Y. Yu, Melanopogenesis: Dark matter of (almost) any mass and baryonic matter from the evaporation of primordial black holes weighing a ton (or less), J. Cosmol. Astropart. Phys. 05 (2019) 005.
  57. D. Hooper, G. Krnjaic, and S. D. McDermott, Dark radiation and superheavy dark matter from black hole domination, J. High Energy Phys. 08 (2019) 001.
  58. A. Chaudhuri and A. Dolgov, PBH evaporation, baryon asymmetry, and dark matter, J. Exp. Theor. Phys. 133, 552 (2021).
  59. I. Masina, Dark matter and dark radiation from evaporating primordial black holes, Eur. Phys. J. Plus 135, 552 (2020).
  60. I. Baldes, Q. Decant, D. C. Hooper, and L. López-Honorez, Non-cold dark matter from primordial black hole evaporation, J. Cosmol. Astropart. Phys. 08 (2020) 045.
  61. P. Gondolo, P. Sandick, and B. Shams Es Haghi, Effects of primordial black holes on dark matter models, Phys. Rev. D 102, 095018 (2020).
  62. N. Bernal and Ó. Zapata, Self-interacting dark matter from primordial black holes, J. Cosmol. Astropart. Phys. 03 (2021) 007.
  63. N. Bernal and Ó. Zapata, Gravitational dark matter production: Primordial black holes and UV freeze-in, Phys. Lett. B 815, 136129 (2021).
  64. N. Bernal and Ó. Zapata, Dark matter in the time of primordial black holes, J. Cosmol. Astropart. Phys. 03 (2021) 015.
  65. N. Bernal, Gravitational dark matter and primordial black holes, arXiv:2105.04372.
  66. A. Cheek, L. Heurtier, Y. F. Pérez-González, and J. Turner, Primordial black hole evaporation and dark matter production. I. Solely Hawking radiation, Phys. Rev. D 105, 015022 (2022).
  67. A. Cheek, L. Heurtier, Y. F. Pérez-González, and J. Turner, Primordial black hole evaporation and dark matter production. II. Interplay with the freeze-in or freeze-out mechanism, Phys. Rev. D 105, 015023 (2022).
  68. N. Bernal, F. Hajkarim, and Y. Xu, Axion dark matter in the time of primordial black holes, Phys. Rev. D 104, 075007 (2021).
  69. N. Bernal, Y. F. Pérez-González, Y. Xu, and Ó. Zapata, ALP dark matter in a primordial black hole dominated universe, Phys. Rev. D 104, 123536 (2021).
  70. N. Bernal, Y. F. Pérez-González, and Y. Xu, Superradiant production of heavy dark matter from primordial black holes, Phys. Rev. D 106, 015020 (2022).
  71. A. Cheek, L. Heurtier, Y. F. Pérez-González, and J. Turner, Redshift effects in particle production from Kerr primordial black holes, Phys. Rev. D 106, 103012 (2022).
  72. K. Mazde and L. Visinelli, The interplay between the dark matter axion and primordial black holes, J. Cosmol. Astropart. Phys. 01 (2023) 021.
  73. A. Cheek, L. Heurtier, Y. F. Pérez-González, and J. Turner, Evaporation of primordial black holes in the early Universe: Mass and spin distributions, Phys. Rev. D 108, 015005 (2023).
  74. G. Arcadi, M. Lindner, J. P. Neto, and F. S. Queiroz, Ultraheavy dark matter and wimps production aided by primordial black holes, arXiv:2408.13313.
  75. R. Allahverdi et al., The first three seconds: A review of possible expansion histories of the early universe, Open J. Astrophys. 4, 10 (2021).
  76. B. Batell et al., Conversations and deliberations: Non-standard cosmological epochs and expansion histories, Int. J. Mod. Phys. A 40, 2530004 (2025).
  77. W. Altmannshofer, S. Gori, S. Profumo, and F. S. Queiroz, Explaining dark matter and B decay anomalies with an Lμ−Lτ model, J. High Energy Phys. 12 (2016) 106.
  78. C.-H. Chen and T. Nomura, Lμ−Lτ gauge-boson production from lepton flavor violating τ decays at Belle II, Phys. Rev. D 96, 095023 (2017).
  79. T. Araki, S. Hoshino, T. Ota, J. Sato, and T. Shimomura, Detecting the Lμ−Lτ gauge boson at Belle II, Phys. Rev. D 95, 055006 (2017).
  80. Y. Zhang, Z. Yu, Q. Yang, M. Song, G. Li, and R. Ding, Probing the Lμ−Lτ gauge boson at electron colliders, Phys. Rev. D 103, 015008 (2021).
  81. Y. Kaneta and T. Shimomura, On the possibility of a search for the Lμ−Lτ gauge boson at Belle-II and neutrino beam experiments, Prog. Theor. Exp. Phys. 2017, 053B04 (2017).
  82. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  83. P. Arias, N. Bernal, A. Herrera, and C. Maldonado, Reconstructing non-standard cosmologies with dark matter, J. Cosmol. Astropart. Phys. 10 (2019) 047.
  84. M. Kawasaki, K. Kohri, and N. Sugiyama, MeV scale reheating temperature and thermalization of neutrino background, Phys. Rev. D 62, 023506 (2000).
  85. S. Hannestad, What is the lowest possible reheating temperature?, Phys. Rev. D 70, 043506 (2004).
  86. R. H. Cyburt, B. D. Fields, K. A. Olive, and T.-H. Yeh, Big Bang nucleosynthesis: 2015, Rev. Mod. Phys. 88, 015004 (2016).
  87. P. F. de Salas, M. Lattanzi, G. Mangano, G. Miele, S. Pastor, and O. Pisanti, Bounds on very low reheating scenarios after Planck, Phys. Rev. D 92, 123534 (2015).
  88. P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis, Nucl. Phys. B360, 145 (1991).
  89. 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.
  90. A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, FeynRules 2.0–A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185, 2250 (2014).
  91. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  92. P. Figueroa, G. Herrera, and F. Ochoa, Direct detection of light dark matter charged under a Lμ−Lτ symmetry, Phys. Rev. D 110, 095018 (2024).
  93. A. H. Abdelhameed et al. (CRESST Collaboration), First results from the CRESST-III low-mass dark matter program, Phys. Rev. D 100, 102002 (2019).
  94. P. Agnes et al. (DarkSide-50 Collaboration), Search for low-mass dark matter WIMPs with 12 ton-day exposure of DarkSide-50, Phys. Rev. D 107, 063001 (2023).
  95. L. Barak et al. (SENSEI Collaboration), SENSEI: Direct-detection results on sub-GeV dark matter from a new skipper-CCD, Phys. Rev. Lett. 125, 171802 (2020).
  96. I. M. Bloch et al. (SENSEI Collaboration), SENSEI at SNOLAB: Single-electron event rate and implications for dark matter, Phys. Rev. Lett. 134, 161002 (2025).
  97. C. Cheng et al. (PandaX-II Collaboration), Search for light dark matter-electron scatterings in the PandaX-II experiment, Phys. Rev. Lett. 126, 211803 (2021).
  98. E. Aprile et al. (XENON Collaboration), Light dark matter search with ionization signals in XENON1T, Phys. Rev. Lett. 123, 251801 (2019).
  99. M. Ackermann et al. (Fermi-LAT Collaboration), Searching for dark matter annihilation from milky way dwarf spheroidal galaxies with six years of fermi large area telescope data, Phys. Rev. Lett. 115, 231301 (2015).
  100. H. Abdalla et al. (H.E.S.S. Collaboration), Search for dark matter annihilation signals in the H.E.S.S. inner galaxy survey, Phys. Rev. Lett. 129, 111101 (2022).
  101. R. K. Leane, T. R. Slatyer, J. F. Beacom, and K. C. Y. Ng, GeV-scale thermal WIMPs: Not even slightly ruled out, Phys. Rev. D 98, 023016 (2018).
  102. T. R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results, Phys. Rev. D 93, 023527 (2016).
  103. C. A. Manzari, J. Martin Camalich, J. Spinner, and R. Ziegler, Supernova limits on muonic dark forces, Phys. Rev. D 108, 103020 (2023).
  104. K. Hirata et al. (Kamiokande-II Collaboration), Observation of a neutrino burst from the supernova SN 1987A, Phys. Rev. Lett. 58, 1490 (1987).
  105. R. M. Bionta et al., Observation of a neutrino burst in coincidence with Supernova SN 1987A in the large magellanic cloud, Phys. Rev. Lett. 58, 1494 (1987).
  106. E. N. Alekseev, L. N. Alekseeva, I. V. Krivosheina, and V. I. Volchenko, Detection of the neutrino signal from SN1987A in the LMC using the Inr Baksan underground scintillation telescope, Phys. Lett. B 205, 209 (1988).
  107. T. J. Loredo and D. Q. Lamb, Bayesian analysis of neutrinos observed from supernova SN-1987A, Phys. Rev. D 65, 063002 (2002).
  108. F. Vissani, Comparative analysis of SN1987A antineutrino fluence, J. Phys. G 42, 013001 (2015).
  109. S. E. Woosley and A. Heger, Nucleosynthesis and remnants in massive stars of solar metallicity, Phys. Rep. 442, 269 (2007).
  110. T. Sukhbold, S. Woosley, and A. Heger, A high-resolution study of presupernova core structure, Astrophys. J. 860, 93 (2018).
  111. https://github.com/spinjo/SNforMuTau
  112. C. Cesarotti and R. Gambhir, The new physics case for beam-dump experiments with accelerated muon beams, J. High Energy Phys. 05 (2024) 283.
  113. S. Airen, E. Broadberry, G. Marques-Tavares, and L. Ricci, Vector portals at future lepton colliders, J. High Energy Phys. 08 (2025) 029.
  114. Y. Kahn, G. Krnjaic, N. Tran, and A. Whitbeck, M3: A new muon missing momentum experiment to probe (g−2)μ and dark matter at Fermilab, J. High Energy Phys. 09 (2018) 153.
  115. H. Davoudiasl, H. Liu, R. Marcarelli, Y. Soreq, and S. Trifinopoulos, New physics at the Muon (synchrotron) ion collider: MuSIC for several scales, J. High Energy Phys. 03 (2025) 046.
  116. G.-y. Huang, F. S. Queiroz, and W. Rodejohann, Gauged Lμ−Lτ at a muon collider, Phys. Rev. D 103, 095005 (2021).
  117. A. Acharyya et al. (CTA Collaboration), Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the galactic centre, J. Cosmol. Astropart. Phys. 01 (2021) 057.
  118. J. Aalbers et al. (DARWIN Collaboration), DARWIN: Towards the ultimate dark matter detector, J. Cosmol. Astropart. Phys. 11 (2016) 017.
  119. L. Baudis, DARWIN/XLZD: A future xenon observatory for dark matter and other rare interactions, Nucl. Phys. B1003, 116473 (2024).
  120. https://wwwmpa.mpa-garching.mpg.de/ccsnarchive/.
  121. Data used in this study: https://github.com/jacintoneto/ThermalDM-EMD-LmuLtau. Embargo applies before 30 December 2025.
  122. G. Mangano, G. Miele, S. Pastor, T. Pinto, O. Pisanti, and P. D. Serpico, Relic neutrino decoupling including flavor oscillations, Nucl. Phys. B729, 221 (2005).
  123. P. F. de Salas and S. Pastor, Relic neutrino decoupling with flavour oscillations revisited, J. Cosmol. Astropart. Phys. 07 (2016) 051.
  124. P. Foldenauer and J. Hoefken Zink, How to rule out (g−2)μ in U(1)Lμ−Lτ with white dwarf cooling, J. High Energy Phys. 07 (2024) 096.
  125. N. F. Bell, G. Busoni, and A. Ghosh, Using neutron stars to probe dark matter charged under a Lμ−Lτ symmetry, arXiv:2505.06506.
  126. S. Baek, N. G. Deshpande, X. G. He, and P. Ko, Muon anomalous g-2 and gauged Lμ−Lτ models, Phys. Rev. D 64, 055006 (2001).
  127. F. S. Queiroz and W. Shepherd, New physics contributions to the Muon anomalous magnetic moment: A numerical code, Phys. Rev. D 89, 095024 (2014).
  128. M. Lindner, M. Platscher, and F. S. Queiroz, A call for new physics: The muon anomalous magnetic moment and lepton flavor violation, Phys. Rep. 731, 1 (2018).
  129. G. Bellini et al., Precision measurement of the Be7 solar neutrino interaction rate in Borexino, Phys. Rev. Lett. 107, 141302 (2011).
  130. M. Bauer, P. Foldenauer, and J. Jaeckel, Hunting all the hidden photons, J. High Energy Phys. 07 (2018) 094.
  131. A. Kamada, K. Kaneta, K. Yanagi, and H.-B. Yu, Self-interacting dark matter and muon g−2 in a gauged U(1)Lμ−Lτ model, J. High Energy Phys. 06 (2018) 117.
  132. S. Gninenko and D. Gorbunov, Refining constraints from Borexino measurements on a light Z’-boson coupled to Lμ−Lτ current, Phys. Lett. B 823, 136739 (2021).
  133. D. Geiregat et al. (CHARM-II Collaboration), First observation of neutrino trident production, Phys. Lett. B 245, 271 (1990).
  134. S. R. Mishra et al. (CCFR Collaboration), Neutrino tridents and W Z interference, Phys. Rev. Lett. 66, 3117 (1991).
  135. W. Altmannshofer, S. Gori, M. Pospelov, and I. Yavin, Neutrino trident production: A powerful probe of new physics with neutrino beams, Phys. Rev. Lett. 113, 091801 (2014).
  136. G. Aad et al. (ATLAS Collaboration), Search for a new Z’ gauge boson in 4μ events with the ATLAS experiment, J. High Energy Phys. 07 (2023) 090.
  137. G. Aad et al. (ATLAS Collaboration), Search for a new Z’ gauge boson via the pp→W±(*)→Z′μ±ν→μ±μ∓μ±ν process in pp collisions at s=13  TeV with the ATLAS detector, Phys. Rev. D 110, 072008 (2024).
  138. Y. M. Andreev et al., First constraints on the Lμ−Lτ explanation of the muon g-2 anomaly from NA64-e at CERN, J. High Energy Phys. 07 (2024) 212.
  139. J. P. Lees et al. (BABAR Collaboration, Search for a muonic dark force at BABAR, Phys. Rev. D 94, 011102 (2016).
  140. I. Adachi et al. (Belle-II Collaboration), Search for a μ+μ− resonance in four-muon final states at Belle II, Phys. Rev. D 109, 112015 (2024).
  141. A. Berlin, N. Blinov, G. Krnjaic, P. Schuster, and N. Toro, Dark matter, millicharges, axion and scalar particles, gauge bosons, and other new physics with LDMX, Phys. Rev. D 99, 075001 (2019).
  142. A. Accardi et al., Electron ion collider: The next QCD frontier: Understanding the glue that binds us all, Eur. Phys. J. A 52, 268 (2016).
  143. E. C. Aschenauer et al., eRHIC design study: An electron-ion collider at BNL, arXiv:1409.1633.
  144. C. Accettura et al. (International Muon Collider Collaboration), The Muon collider, arXiv:2504.21417.

Outline

Information

Phys. Rev. D 112, 075042– Published 22 October, 2025
  • Received 8 July 2025
  • Accepted 28 September 2025
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