Abstract
To ensure anomaly cancellation, the E6 inspired U(1) extensions of the Minimal Supersymmetric (SUSY) Standard Model (MSSM) involve extra exotic matter. The lightest exotic neutralino in these models can be stable contributing to the cold dark matter density. We consider the interactions of such neutralino with nucleons within a specific extension of the MSSM with an additional U(1)N gauge symmetry (SE6SSM). The constraints on the couplings of this state, which are set by the present experimental bounds caused by the direct detection experiments, are examined. The obtained results can be generalised to other E6 inspired SUSY models with extra U(1) gauge symmetry.
References
[1] P. A. R. Ade et al. (Planck Collaboration), Planck 2015 results. XIII. Cosmological parameters, Astronomy & Astrophysics 594 (2016) A13.
[2] G. R. Blumenthal, S. M. Faber, J. R. Primack, M. J. Rees, Formation of galaxies and large scale structure with cold dark matter, Nature 311 (1984) 517–525.
[3] J. R. Primack, Status of cold dark matter cosmology, Nuclear Physics B — Proceedings Supplements 124 (2003) 3–12.
[4] G. Jungman, M. Kamionkowski, K. Griest, Supersymmetric dark matter, Physics Reports 267 (1996) 195–373.
[5] J. R. Ellis, S. Kelley, D. V. Nanopoulos, Probing the desert using gauge coupling unification, Physics Letters B 260 (1991) 131–137.
[6] P. Langacker, M. X. Luo, Implications of precision electroweak experiments for Mt, ρ0, sin2 θW and grand unification, Physical Review D 44 (1991) 817–822.
[7] U. Amaldi, W. de Boer, H. Furstenau, Comparison of grand unified theories with electroweak and strong coupling constants measured at LEP, Physics Letters B 260 (1991) 447–455.
[8] F. Anselmo, L. Cifarelli, A. Peterman, A. Zichichi, The effective experimental constraints on Msusy and Mgut, Nuovo Cimento A 104 (1991) 1817–1834.
[9] H. Georgi, S. L. Glashow, Unity of all elementary particle forces, Physical Review Letters 32 (1974) 438.
[10] M. B. Green, J. H. Schwarz, E. Witten, Superstring Theory, Cambridge University Press, 1987.
[11] J. L. Hewett, T. G. Rizzo, Low-energy phenomenology of superstring inspired E6 models, Physics Reports 183 (1989) 193.
[12] P. Langacker, The physics of heavy Z′ gauge bosons, Reviews of Modern Physics 81 (2009) 1199.
[13] R. B. Nevzorov, Phenomenological aspects of supersymmetric extensions of the Standard Model, Uspekhi Fizicheskikh Nauk 193 (6) (2023) 577–613.
[14] J. Kang, P. Langacker, B. D. Nelson, Theory and phenomenology of exotic isosinglet quarks and squarks, Physical Review D 77 (2008) 035003.
[15] M. Ali, S. Khalil, S. Moretti, S. Munir, R. Nevzorov, A. Nikitenko, H. Waltari, TeV-scale leptoquark searches at the LHC and their E6SSM interpretation, Journal of High Energy Physics 03 (2023) 117.
[16] E. Accomando, A. Belyaev, L. Fedeli, S. F. King, C. Shepherd-Themistocleous, Z′ physics with early LHC data, Physical Review D 83 (2011) 075012.
[17] J. H. Kang, P. Langacker, T. J. Li, Neutrino masses in supersymmetric SU(3)C × SU(2)L × U(1)Y × U(1)′ models, Physical Review D 71 (2005) 015012.
[18] E. Ma, Neutrino masses in an extended gauge model with E6 particle content, Physics Letters B 380 (1996) 286.
[19] B. Stech, Z. Tavartkiladze, Generation symmetry and E6 unification, Physical Review D 77 (2008) 076009.
[20] E. Ma, M. Raidal, Three active and two sterile neutrinos in an E6 model of diquark baryogenesis, Journal of Physics G 28 (2002) 95–102.
[21] J. Kang, P. Langacker, T. J. Li, T. Liu, Electroweak baryogenesis in a supersymmetric U(1)′ model, Physical Review Letters 94 (2005) 061801.
[22] R. Nevzorov, Leptogenesis as an origin of hot dark matter and baryon asymmetry in the E6 inspired SUSY models, Physics Letters B 779 (2018) 223–229.
[23] R. Nevzorov, Leptogenesis and dark matter-nucleon scattering cross section in the SE6SSM, Universe 9 (3) (2023) 137.
[24] T. Hambye, E. Ma, M. Raidal, U. Sarkar, Allowable low-energy E6 subgroups from leptogenesis, Physics Letters B 512 (2001) 373.
[25] S. F. King, R. Luo, D. J. Miller, R. Nevzorov, Leptogenesis in the exceptional supersymmetric Standard Model: Flavour dependent lepton asymmetries, Journal of High Energy Physics 12 (2008) 042.
[26] J. A. Grifols, J. Sola, A. Mendez, Contribution to the muon anomaly from superstring inspired models, Physical Review Letters 57 (1986) 2348.
[27] D. A. Morris, Potentially large contributions to the muon anomalous magnetic moment from weak isosinglet squarks in E6 superstring models, Physical Review D 37 (1988) 2012.
[28] S. W. Ham, J. O. Im, E. J. Yoo, S. K. Oh, Higgs bosons of a supersymmetric E6 model at the Large Hadron Collider, Journal of High Energy Physics 12 (2008) 017.
[29] P. Langacker, J. Wang, U(1)′ symmetry breaking in supersymmetric E6 models, Physical Review D 58 (1998) 115010.
[30] M. Cvetic, P. Langacker, New gauge bosons from string models, Modern Physics Letters A 11 (1996) 1247–1262.
[31] M. Cvetic, P. Langacker, Implications of Abelian extended gauge structures from string models, Physical Review D 54 (1996) 3570–3579.
[32] M. Cvetic, D. A. Demir, J. R. Espinosa, L. L. Everett, P. Langacker, Electroweak breaking and the µ problem in supergravity models with an additional U(1), Physical Review D 56 (1997) 2861.
[33] D. Suematsu, Y. Yamagishi, Radiative symmetry breaking in a supersymmetric model with an extra U(1), International Journal of Modern Physics A 10 (1995) 4521.
[34] Y. Daikoku, D. Suematsu, Mass bound of the lightest neutral Higgs scalar in the extra U(1) models, Physical Review D 62 (2000) 095006.
[35] E. Keith, E. Ma, Generic consequences of a supersymmetric U(1) gauge factor at the TeV scale, Physical Review D 56 (1997) 7155.
[36] D. Suematsu, µ → eγ in supersymmetric multi U(1) models with an Abelian gaugino mixing, Physics Letters B 416 (1998) 108.
[37] D. Suematsu, Effect on the electron EDM due to Abelian gauginos in SUSY extra U(1) models, Modern Physics Letters A 12 (1997) 1709.
[38] A. Gutierrez-Rodriguez, M. A. Hernandez-Ruiz, M. A. Perez, Limits on the electromagnetic and weak dipole moments of the tau lepton in E6 superstring models, International Journal of Modern Physics A 22 (2007) 3493.
[39] D. Suematsu, Neutralino decay in the µ problem solvable extra U(1) models, Physical Review D 57 (1998) 1738.
[40] E. Keith, E. Ma, Efficacious extra U(1) factor for the supersymmetric Standard Model, Physical Review D 54 (1996) 3587.
[41] S. Hesselbach, F. Franke, H. Fraas, Neutralinos in E6 inspired supersymmetric U(1)′ models, The European Physical Journal C 23 (2002) 149–162.
[42] V. Barger, P. Langacker, H. S. Lee, Lightest neutralino in extensions of the MSSM, Physics Letters B 630 (2005) 85–99.
[43] S. Y. Choi, H. E. Haber, J. Kalinowski, P. M. Zerwas, The neutralino sector in the U(1)-extended supersymmetric Standard Model, Nuclear Physics B 778 (2007) 85–128.
[44] V. Barger, P. Langacker, I. Lewis, M. McCaskey, G. Shaughnessy, B. Yencho, Recoil detection of the lightest neutralino in MSSM singlet extensions, Physical Review D 75 (2007) 115002.
[45] T. Gherghetta, T. A. Kaeding, G. L. Kane, Supersymmetric contributions to the decay of an extra Z boson, Physical Review D 57 (1998) 3178.
[46] V. Barger, P. Langacker, G. Shaughnessy, TeV physics and the Planck scale, New Journal of Physics 9 (2007) 333.
[47] V. Barger, P. Langacker, H. S. Lee, G. Shaughnessy, Higgs sector in extensions of the MSSM, Physical Review D 73 (2006) 115010.
[48] S. F. King, S. Moretti, R. Nevzorov, Theory and phenomenology of an exceptional supersymmetric Standard Model, Physical Review D 73 (2006) 035009.
[49] S. F. King, S. Moretti, R. Nevzorov, Exceptional supersymmetric Standard Model, Physics Letters B 634 (2006) 278.
[50] S. F. King, S. Moretti, R. Nevzorov, Spectrum of Higgs Particles in the ESSM, in: Proceedings of the 12th Lomonosov Conference on Elementary Particle Physics, World Scientific Company, Moscow, Russia, 2005, p. 371.
[51] S. F. King, S. Moretti, R. Nevzorov, A review of the exceptional supersymmetric Standard Model, Symmetry 12 (4) (2020) 557.
[52] R. Nevzorov, E6 inspired supersymmetric models with exact custodial symmetry, Physical Review D 87 (2013) 015029.
[53] P. Athron, M. M¨uhlleitner, R. Nevzorov, A. G. Williams, Non-standard Higgs decays in U(1) extensions of the MSSM, Journal of High Energy Physics 01 (2015) 153.
[54] P. Athron, D. Harries, R. Nevzorov, A. G. Williams, E6 inspired SUSY benchmarks, dark matter relic density and a 125 GeV Higgs, Physics Letters B 760 (2016) 19–25.
[55] P. Athron, D. Harries, R. Nevzorov, A. G. Williams, Dark matter in a constrained E6 inspired SUSY model, Journal of High Energy Physics 12 (2016) 128.
[56] R. Nevzorov, On the suppression of the dark matter-nucleon scattering cross section in the SE6SSM, Symmetry 14 (10) (2022) 2090.
[57] J. Aalbers et al. (LZ), Dark matter search results from 4.2 tonne-years of exposure of the LUX–ZEPLIN (LZ) experiment, Physical Review Letters 135 (2025) 011802.
[58] R. Howl, S. F. King, Planck scale unification in a supersymmetric Standard Model, Physics Letters B 652 (2007) 331.
[59] R. Howl, S. F. King, Minimal E6 supersymmetric Standard Model, Journal of High Energy Physics 01 (2008) 030.
[60] R. Howl, S. F. King, Exceptional supersymmetric Standard Models with non-Abelian discrete family symmetry, Journal of High Energy Physics 05 (2008) 008.
[61] R. Howl, S. F. King, Solving the flavour problem in supersymmetric Standard Models with three Higgs families, Physics Letters B 687 (2010) 355.
[62] P. Athron, J. P. Hall, R. Howl, S. F. King, D. J. Miller, S. Moretti, R. Nevzorov, Aspects of the exceptional supersymmetric Standard Model, Nuclear Physics B — Proceedings Supplements 200–202 (2010) 120.
[63] J. P. Hall, S. F. King, Bino Dark Matter and Big Bang Nucleosynthesis in the constrained E6SSM with massless inert singlinos, Journal of High Energy Physics 06 (2011) 006.
[64] J. C. Callaghan, S. F. King, E6 models from F-theory, Journal of High Energy Physics 04 (2013) 034.
[65] J. C. Callaghan, S. F. King, G. K. Leontaris, Gauge coupling unification in E6 F-theory GUTs with matter and bulk exotics from flux breaking, Journal of High Energy Physics 12 (2013) 037.
[66] S. F. King, R. Nevzorov, 750 GeV diphoton resonance from singlets in an exceptional supersymmetric Standard Model, Journal of High Energy Physics 03 (2016) 139.
[67] R. Nevzorov, E6 inspired SUSY models with custodial symmetry, International Journal of Modern Physics A 33 (2018) 1844007.
[68] S. Khalil, S. Moretti, D. Rojas-Ciofalo, H. Waltari, Multicomponent dark matter in a simplified E6SSM, Physical Review D 102 (2020) 075039.
[69] S. F. King, S. Moretti, R. Nevzorov, Gauge coupling unification in the exceptional supersymmetric Standard Model, Physics Letters B 650 (2007) 57–64.
[70] R. Nevzorov, Quasifixed point scenarios and the Higgs mass in the E6 inspired supersymmetric models, Physical Review D 89 (2014) 055010.
[71] R. Nevzorov, M. A. Trusov, Infrared quasifixed solutions in the NMSSM, Physics of Atomic Nuclei 64 (2001) 1299.
[72] R. Nevzorov, M. A. Trusov, Quasifixed point scenario in the modified NMSSM, Physics of Atomic Nuclei 65 (2002) 335.
[73] C. D. Froggatt, R. Nevzorov, H. B. Nielsen, D. Thompson, Fixed point scenario in the Two Higgs Doublet Model inspired by degenerate vacua, Physics Letters B 657 (2007) 95–102.
[74] S. F. King, S. Moretti, R. Nevzorov, E6SSM, AIP Conference Proceedings 881 (2007) 138–143.
[75] A. Belyaev, J. P. Hall, S. F. King, P. Svantesson, Novel gluino cascade decays in E6 inspired models, Physical Review D 86 (2012) 031702.
[76] A. Belyaev, J. P. Hall, S. F. King, P. Svantesson, Discovering E6 supersymmetric models in gluino cascade decays at the LHC, Physical Review D 87 (2013) 035019.
[77] R. Nevzorov, S. Pakvasa, Exotic Higgs decays in the E6 inspired SUSY models, Physics Letters B 728 (2014) 210–215.
[78] J. P. Hall, S. F. King, R. Nevzorov, S. Pakvasa, M. Sher, Novel Higgs decays and dark matter in the E6SSM, Physical Review D 83 (2011) 075013.
[79] J. P. Hall, S. F. King, R. Nevzorov, S. Pakvasa, M. Sher, Nonstandard Higgs decays in the E6SSM, PoS QFTHEP2010 (2010) 069.
[80] R. Nevzorov, S. Pakvasa, Nonstandard Higgs decays in the E6 inspired SUSY models, Nuclear and Particle Physics Proceedings 273–275 (2016) 690–695.
[81] R. Nevzorov, Higgs boson with mass around 125 GeV in SUSY extensions of the SM, Physics of Atomic Nuclei 83 (2) (2020) 338–350.
[82] P. Athron, M. Muhlleitner, R. Nevzorov, A. G. Williams, Exotic Higgs Decays in U(1) Extensions of the MSSM, in: Proceedings of the 17th Lomonosov Conference on Elementary Particle Physics, World Scientific Company, Moscow, Russia, 2015, p. 487.
[83] R. Nevzorov, LHC signatures and cosmological implications of the E6 inspired SUSY models, PoS EPS-HEP2015 (2015) 381.
[84] S. Hesselbach, D. J. Miller, G. Moortgat-Pick, R. Nevzorov, M. Trusov, The Lightest Neutralino in the MNSSM, in: Proceedings of the 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY07), Karlsruhe, Germany, 2007, p. 918.
[85] S. Hesselbach, D. J. Miller, G. Moortgat-Pick, R. Nevzorov, M. Trusov, Theoretical upper bound on the mass of the LSP in the MNSSM, Physics Letters B 662 (2008) 199–207.
[86] J. M. Frere, R. B. Nevzorov, M. I. Vysotsky, Stimulated neutrino conversion and bounds on neutrino magnetic moments, Physics Letters B 394 (1997) 127–131.
[87] M. Bolz, A. Brandenburg, W. Buchmuller, Thermal production of gravitinos, Nuclear Physics B 606 (2001) 518.
[88] H. Eberl, I. D. Gialamas, V. C. Spanos, Gravitino thermal production revisited, Physical Review D 103 (2021) 075025.
[89] A. Hook, R. McGehee, H. Murayama, Cosmologically viable low-energy supersymmetry breaking, Physical Review D 98 (2018) 115036.
[90] S. Khalil, S. Moretti, D. Rojas-Ciofalo, H. Waltari, Monophoton signals at e+e− colliders in a simplified E6SSM, Physical Review D 104 (2021) 035008.
[91] S. Khalil, K. Kowalska, S. Moretti, D. Rojas-Ciofalo, H. Waltari, A combined approach to the analysis of space and ground experimental data within a simplified E6SSM, The European Physical Journal C 82 (2022) 1058.
[92] P. A. Kovalenko, R. B. Nevzorov, K. A. Ter-Martirosian, Masses of Higgs bosons in supersymmetric theories, Physics of Atomic Nuclei 61 (1998) 812–824.
[93] R. B. Nevzorov, M. A. Trusov, Particle spectrum in the modified NMSSM in the strong Yukawa coupling limit, Journal of Experimental and Theoretical Physics 91 (6) (2000) 1079–1097.
[94] R. B. Nevzorov, K. A. Ter-Martirosyan, M. A. Trusov, Higgs bosons in the simplest SUSY models, Physics of Atomic Nuclei 65 (2002) 285–298.
[95] N. Arkani-Hamed, A. Delgado, G. F. Giudice, The well-tempered neutralino, Nuclear Physics B 741 (2006) 108.
[96] G. Chalons, M. J. Dolan, C. McCabe, Neutralino dark matter and the Fermi gamma-ray lines, Journal of Cosmology and Astroparticle Physics 02 (2013) 016.
[97] G. Belanger, F. Boudjema, A. Pukhov, A. Semenov, MicrOMEGAs3: A program for calculating dark matter observables, Computer Physics Communications 185 (2014) 960.
[98] H. W. Lin, R. Gupta, B. Yoon, Y. C. Jang, T. Bhattacharya, Quark contribution to the proton spin from 2 + 1 + 1-flavor lattice QCD, Physical Review D 98 (2018) 094512.
[99] A. M. Sirunyan et al. (CMS), Search for resonant and nonresonant new phenomena in high-mass dilepton final states at √ s = 13 TeV, Journal of High Energy Physics 07 (2021) 208.
[100] G. Aad et al. (ATLAS), Search for high-mass dilepton resonances using 139 fb−1 of pp collision data collected at √ s = 13 TeV with the ATLAS detector, Physics Letters B 796 (2019) 68–87.
[101] R. Abbasi et al. (IceCube), Search for high-energy neutrinos from the Sun using ten years of IceCube data. arXiv:2507.08457 (hep-ex).
[102] H. Baer, V. Barger, D. Sengupta, X. Tata, Is natural Higgsino-only dark matter excluded?, The European Physical Journal C 78 (2018) 838.
[103] H. Baer, V. Barger, P. Huang, A. Mustafayev, X. Tata, Radiative natural SUSY with a 125 GeV Higgs boson, Physical Review Letters 109 (2012) 161802.
[104] H. Baer, V. Barger, P. Huang, X. Tata, Natural supersymmetry: LHC, dark matter and ILC searches, Journal of High Energy Physics 05 (2012) 109.
[105] H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev, X. Tata, Radiative natural supersymmetry: Reconciling electroweak fine tuning and the Higgs boson mass, Physical Review D 87 (2013) 115028.
[106] G. Aad et al. (ATLAS), Searches for electroweak production of supersymmetric particles with compressed mass spectra in √s = 13 TeV pp collisions with the ATLAS detector, Physical Review D 101 (2020) 052005.
[107] A. M. Sirunyan et al. (CMS), Search for supersymmetry with a compressed mass spectrum in the vector boson fusion topology with 1-lepton and 0-lepton final states in proton–proton collisions at √s = 13 TeV, Journal of High Energy Physics 08 (2019) 150.
[108] M. Aaboud et al. (ATLAS), Search for heavy charged long-lived particles in the ATLAS detector in 36.1 fb−1 of proton–proton collision data at √s = 13 TeV, Physical Review D 99 (2019) 092007.
[109] N. Nagata, S. Shirai, Higgsino dark matter in high-scale supersymmetry, Journal of High Energy Physics 01 (2015) 029.
[110] M. Cirelli, N. Fornengo, A. Strumia, Minimal dark matter, Nuclear Physics B 753 (2006) 178.