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Journal of Low Temperature Physics

, Volume 175, Issue 1–2, pp 486–497 | Cite as

Higgs Bosons in Particle Physics and in Condensed Matter

  • G. E. Volovik
  • M. A. Zubkov
Article

Abstract

Higgs bosons—the amplitude modes—have been experimentally investigated in condensed matter for many years. An example is superfluid 3He-B, where the broken symmetry leads to 4 Goldstone modes and at least 14 Higgs modes, which are characterized by angular momentum quantum number J and parity (Zeeman splitting of Higgs modes with J=2+ and J=2 in magnetic field has been observed in 80’s). Based on the relation \(E_{J+}^{2}+E_{J-}^{2}=4\varDelta^{2}\) for the energy spectrum of these modes, Yoichiro Nambu proposed the general sum rule, which relates masses of Higgs bosons and masses of fermions. If this rule is applicable to Standard Model, one may expect that the observed Higgs boson with mass M H1=125 GeV has a Nambu partner—the second Higgs boson with mass M H2=325 GeV. Together they satisfy the Nambu relation \(M_{\mathrm{H}1}^{2} + M_{\mathrm{H}2}^{2} = 4 M_{\mathrm{top}}^{2}\), where M top is the top quark mass. Also the properties of the Higgs modes in superfluid 3He-A, where the symmetry breaking is similar to that of the Standard Model, suggest the possible existence of two electrically charged Higgs particles with masses M H+=M H−∼245 GeV, which together obey the Nambu rule \(M_{\mathrm{H}+}^{2} + M_{\mathrm{H}-}^{2} = 4 M_{\mathrm{top}}^{2}\). A certain excess of events at 325 GeV and at 245 GeV has been reported in 2011, though not confirmed in 2012 experiments. Besides, we consider the particular relativistic model of top—quark condensation that suggests the possibility that two twice degenerated Higgs bosons contribute to the Nambu sum rule. This gives the mass around 210 GeV for the Nambu partner of the 125 GeV Higgs boson. We also discuss the other possible lessons from the condensed matter to Standard Model, such as hidden symmetry, where light Higgs emerges as quasi Nambu-Goldstone mode, and the role of broken time reversal symmetry.

Keywords

Higgs boson Standard model Goldstone modes Superfluid 3He 

Notes

Acknowledgements

This work was partly supported by RFBR grant 11-02-01227, by the Federal Special-Purpose Programme ‘Human Capital’ of the Russian Ministry of Science and Education. GEV acknowledges a financial support of the Academy of Finland and its COE program, and the EU FP7 program (#228464 Microkelvin).

References

  1. 1.
    P.W. Anderson, Phys. Rev. 130, 439–442 (1963) ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    F. Englert, R. Brout, Phys. Rev. Lett. 13, 321–323 (1964) ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    P. Higgs, Phys. Rev. Lett. 13, 508–509 (1964) ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    G. Guralnik, C.R. Hagen, T.W.B. Kibble, Phys. Rev. Lett. 13, 585–587 (1964) ADSCrossRefGoogle Scholar
  5. 5.
    T. Lawson, W.J. Gully, S. Goldstein, R.C. Richardson, D.M. Lee, Phys. Rev. Lett. 30, 541 (1973) ADSCrossRefGoogle Scholar
  6. 6.
    D.W. Paulson, R.T. Johnson, J.C. Wheatley, Phys. Rev. Lett. 30, 829 (1973) ADSCrossRefGoogle Scholar
  7. 7.
    P.B. Littlewood, C.M. Varma, Phys. Rev. Lett. 47, 811 (1981) ADSCrossRefGoogle Scholar
  8. 8.
    M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schaub, C. Gross, E. Demler, S. Kuhr, I. Bloch, Nature 487, 455–458 (2012) ADSCrossRefGoogle Scholar
  9. 9.
    S. Gazit, D. Podolsky, A. Auerbach, arXiv:1212.3759
  10. 10.
    Y. Barlas, C.M. Varma, Phys. Rev. B 87, 054503 (2013) ADSCrossRefGoogle Scholar
  11. 11.
    K. Chen, L. Liu, Y. Deng, L. Pollet, N. Prokof’ev, Phys. Rev. Lett. 110, 170403 (2013) ADSCrossRefGoogle Scholar
  12. 12.
    R. Matsunaga, Y.I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, R. Shimano, arXiv:1305.0381
  13. 13.
    Y. Nambu, Physica D 15, 147–151 (1985) ADSCrossRefGoogle Scholar
  14. 14.
    Y. Nambu, in BCS: 50 Years, ed. by L.N. Cooper, D. Feldman (World Scientific, Singapore, 2010) Google Scholar
  15. 15.
    Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345–358 (1961) ADSCrossRefGoogle Scholar
  16. 16.
    D. Vollhardt, P. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990) Google Scholar
  17. 17.
    Y.A. Vdovin, in Applications of Methods of Quantum Field Theory to Many Body Problems, ed. by A.I. Alekseyeva (Gosatomizdat, Moscow, 1963), p. 94 Google Scholar
  18. 18.
    K. Maki, J. Low Temp. Phys. 16, 465 (1974) ADSCrossRefGoogle Scholar
  19. 19.
    K. Nagai, Prog. Theor. Phys. 54, 1–18 (1975) ADSCrossRefGoogle Scholar
  20. 20.
    L. Tewordt, D. Einzel, Phys. Lett. A 56, 97 (1976) ADSCrossRefGoogle Scholar
  21. 21.
    G.E. Volovik, M.A. Zubkov, Pis’ma Zh. Eksp. Teor. Fiz. 97, 344–349 (2013) Google Scholar
  22. 22.
    G.E. Volovik, M.A. Zubkov, Phys. Rev. D 87, 075016 (2013) ADSCrossRefGoogle Scholar
  23. 23.
    O. Avenel, E. Varoquaux, H. Ebisawa, Phys. Rev. Lett. 45, 1952 (1980) ADSCrossRefGoogle Scholar
  24. 24.
    R. Movshovich, E. Varoquaux, N. Kim, D.M. Lee, Phys. Rev. Lett. 61, 1732–1735 (1988) ADSCrossRefGoogle Scholar
  25. 25.
    C.A. Collett, J. Pollanen, J.I.A. Li, W.J. Gannon, W.P. Halperin, J. Low Temp. Phys. 171(3–4), 214–219 (2013). doi: 10.1007/s10909-012-0692-6 ADSCrossRefGoogle Scholar
  26. 26.
    T. Aaltonen et al. (The CDF Collaboration), Phys. Rev. D 85, 012008 (2012) ADSCrossRefGoogle Scholar
  27. 27.
    S. Chatrchyan et al. (CMS Collaboration), Phys. Rev. Lett. 108, 111804 (2012) ADSCrossRefGoogle Scholar
  28. 28.
    K.A. Meissner, H. Nicolai, Phys. Lett. B 718, 943–945 (2013) ADSCrossRefGoogle Scholar
  29. 29.
    L. Maiani, A.D. Polosa, V. Riquer, New J. Phys. 14, 073029 (2012) ADSCrossRefGoogle Scholar
  30. 30.
    P.N. Brusov, V.N. Popov, JETP 53, 804–810 (1981) Google Scholar
  31. 31.
    ATLAS Collaboration, Phys. Lett. B 716, 1–29 (2012) ADSCrossRefGoogle Scholar
  32. 32.
    N.D. Mermin, V.P. Mineev, G.E. Volovik, J. Low Temp. Phys. 33, 117 (1978) ADSCrossRefGoogle Scholar
  33. 33.
    G.E. Volovik, M.V. Khazan, JETP 55, 867 (1982) Google Scholar
  34. 34.
    G.E. Volovik, M.V. Khazan, JETP 58, 551 (1983) Google Scholar
  35. 35.
    G.E. Volovik, Exotic Properties of Superfluid 3He (World Scientific, Singapore, 1992) CrossRefGoogle Scholar
  36. 36.
    H. Watanabe, H. Murayama, Phys. Rev. Lett. 108, 251602 (2012) ADSCrossRefGoogle Scholar
  37. 37.
    H. Watanabe, T. Brauner, H. Murayama, arXiv:1303.1527
  38. 38.
    A. Kapustin, arXiv:1207.0457
  39. 39.
    S. Uchino, M. Kobayashi, M. Nitta, M. Ueda, Phys. Rev. Lett. 105, 230406 (2010) ADSCrossRefGoogle Scholar
  40. 40.
    S.P. Novikov, Russ. Math. Surv. 37, 1–56 (1982) CrossRefMATHGoogle Scholar
  41. 41.
    K. Enqvist, A. Mazumdar, Phys. Rep. 380, 99 (2003) ADSCrossRefMATHMathSciNetGoogle Scholar
  42. 42.
    R. Ling, J. Saunders, W. Wojtanowski, E.R. Dobbs, Euro. Phys. Lett. 10, 323 (1989) ADSCrossRefGoogle Scholar
  43. 43.
    F.R. Klinkhamer, G.E. Volovik, Int. J. Mod. Phys. A 20, 2795–2812 (2005) ADSCrossRefMATHGoogle Scholar
  44. 44.
    M. Shifman, A. Yung, Phys. Rev. Lett. 110, 201602 (2013) ADSCrossRefGoogle Scholar
  45. 45.
    M. Nitta, M. Shifman, W. Vinci, Phys. Rev. D 87, 081702 (2013) ADSCrossRefGoogle Scholar
  46. 46.
    M.A. Zubkov, arXiv:1301.6971
  47. 47.
    V.A. Miransky, M. Tanabashi, K. Yamawaki, Phys. Lett. B 221, 177–183 (1989) ADSCrossRefGoogle Scholar
  48. 48.
    V.A. Miransky, M. Tanabashi, K. Yamawaki, Mod. Phys. Lett. A 4, 1043–1053 (1989) ADSCrossRefGoogle Scholar
  49. 49.
    D. Carmi, A. Falkowski, E. Kuflik, T. Volansky, J. Zupan, arXiv:1207.1718
  50. 50.
    F.R. Klinkhamer, G.E. Volovik, Phys. Rev. D 77, 085015 (2008) ADSCrossRefGoogle Scholar
  51. 51.
    G.E. Volovik, in Proceedings of the 11th MG Meeting on General Relativity, ed. by H. Kleinert, R.T. Jantzen, R. Ruffini (World Scientific, Singapore, 2008), p. 1404 Google Scholar
  52. 52.
    G.E. Volovik, JETP Lett. 82, 319–324 (2005) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.O.V. Lounasmaa Laboratory, School of Science and TechnologyAalto UniversityEspooFinland
  2. 2.L.D. Landau Institute for Theoretical PhysicsMoscowRussia
  3. 3.Institute for Theoretical and Experimental PhysicsMoscowRussia

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