Skip to main content
SpringerLink
Log in

Spontaneous symmetry breaking and massive photons from a Fresnel-type potential

  • Published:
Pramana Aims and scope Submit manuscript

A Correction to this article was published on 17 February 2023

This article has been updated

Abstract

We discuss spontaneous symmetry breaking in the presence of a new type of symmetric potential based on Fresnel integrals which give an infinite number of minima. Several interesting points were raised, in particular the emergence of massive Goldstone boson and an enhancement of the photon mass. The new theory depends on discrete numbers \(n,N\in {\textrm{Z }}\) and hence a large family of massive particles may be obtained filling the gap between the electroweak scale and the Planck scale in the standard model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Change history

References

  1. G Aad et al, Phys. Lett. B 716, 1 (2012)

    Article  ADS  Google Scholar 

  2. S Chatrchyan et al, Phys. Lett. B 716, 30 (2012)

    Article  ADS  Google Scholar 

  3. C Patrignani et al, Chin. Phys. C 40, 100001 (2016)

    Article  ADS  Google Scholar 

  4. M Abdullah, Searching for physics beyond the standard model and beyond, Ph.D. Thesis (University of California, Irvine, 2017)

  5. I Nandori, arXiv:1108.4643

  6. M Bounakis and I G Moss, J. High Energy Phys. 2018, 71 (2018)

    Article  Google Scholar 

  7. N Fonseca, E Morgante and G Servant, J. High Energy Phys. 2018, 20 (2018)

    Article  Google Scholar 

  8. I G Márián, N Defenu, U D Jentschura, A Trombettoni and I Nándori, Nucl. Phys. B 945, 114642 (2019)

    Article  Google Scholar 

  9. O L Trinhammer, Europhys. Lett. 130, 29002 (2020)

    Article  ADS  Google Scholar 

  10. R A El-Nabulsi, Eur. Phys. J. Plus 129, 220 (2014)

    Article  Google Scholar 

  11. A A García, K Bondarenko, S Ploeckinger, J Pradler and A Sokolenko, J. Cosmol. Astropart. Phys. 10, 011 (2020)

    Article  Google Scholar 

  12. P Agrawal, D Saha, L X Xu, J H Yu and C P Yuan, Phys. Rev. D 101, 075023 (2020)

    Article  ADS  Google Scholar 

  13. C Delaunay, C Grojean and J D Wells, J. High Energy Phys. 0804, 029 (2008)

    Article  ADS  Google Scholar 

  14. A Brignole, Nucl. Phys. B 579, 101 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  15. R Sondenheimer, Renormalization group flow of the Higgs sector (vorgelegt dem Rat der Physikalisch-Astronomischen Fakultät der Friedrich-Schiller-Universität Jena, 2016)

  16. L Di Luzio, G Isidori and G Ridolfi, Phys. Lett. B 753, 160 (2016)

    Article  Google Scholar 

  17. M B Einhorn and D R Timothy Jones, J. High Energy Phys. 04, 051 (2007)

    Article  ADS  Google Scholar 

  18. G Isidori, G Ridolfi and A Strumia, Nucl. Phys. B 609, 387 (2001)

    Article  ADS  Google Scholar 

  19. J R Espinosa and M Quiros, Phys. Lett. B 353, 257 (1995)

    Article  ADS  Google Scholar 

  20. G Altarelli and G Isidori, Phys. Lett. B 337, 141 (1994)

    Article  ADS  Google Scholar 

  21. R A El-Nabulsi, Z. Naturforsch. 73, 363 (2018)

    Article  ADS  Google Scholar 

  22. R A El-Nabulsi, Z. Naturforsch. 70, 685 (2015)

    Article  ADS  Google Scholar 

  23. K E Williams, H Rzehak and G Weiglein, Eur. Phys. J. C 71, 1669 (2011)

    Article  ADS  Google Scholar 

  24. I L Buchbinder, M Cvetic and A Y Petrov, Nucl. Phys. B 571, 358 (2000)

    Article  ADS  Google Scholar 

  25. S Bielleman, L E Ibanez, F G Pedro and I Valenzuela, Eur. Phys. J. C 2016, 128 (2016)

    Google Scholar 

  26. A Avgoustidis, S Cremonini, A C Davis, R H Ribeiro, K Turzynski and S Watson, J. Cosmol. Astropart. Phys. 02, 038 (2012)

    Article  ADS  Google Scholar 

  27. I Huston and A J Christopherson, Phys. Rev. D 85, 063507 (2012)

    Article  ADS  Google Scholar 

  28. R A El-Nabulsi, Can. J. Phys. 99, 275 (2021)

    Article  ADS  Google Scholar 

  29. C Grojean, G Servant and J Wells, Phys. Rev. D 71, 036001 (2005)

    Article  ADS  Google Scholar 

  30. B Grinstein and M Trott, Phys. Rev. D 78, 075002 (2008)

    Article  ADS  Google Scholar 

  31. J R Espinosa, B Gripaios, Konstandin and F Riva, J. Cosmol. Astropart. Phys. 01, 012 (2012)

    Article  ADS  Google Scholar 

  32. K G Klimenko, Theor. Math. Phys. 62, 58 (1985)

    Article  Google Scholar 

  33. S Chigusa, T Moroi and Y Shoji, Phys. Rev. D 97, 116012 (2018)

    Article  ADS  Google Scholar 

  34. T Markkanen, A Rajentie and S Stopyra, Front. Astron. Space Sci. 5, 40 (2018)

    Article  ADS  Google Scholar 

  35. V A Bednyakov, N D Giokaris and A V Bednyakov, Phys. Part. Nucl. 39, 13 (2008)

    Article  Google Scholar 

  36. M F M Lutz, Y Heo and X Y Guo, Eur. Phys. J. C 80, 322 (2020)

    Article  ADS  Google Scholar 

  37. S R Coleman and E K Weinberg, Phys. Rev. D 7, 1888 (1973)

    Article  ADS  Google Scholar 

  38. D Buttazzo, G Degrassi, P P Giardino, G F Giudice, F Sala, A Salvio and A Strumia, J. High Energy Phys. 12, 089 (2013)

    Article  ADS  Google Scholar 

  39. J R Espinosa, D Racco and A Riotto, Phys. Rev. Lett. 120, 121301 (2018)

    Article  ADS  Google Scholar 

  40. R A El-Nabulsi, Mod. Phys. Lett. A 36, 2150042 (2021)

    Article  ADS  Google Scholar 

  41. H Watanabe, T Brauner and H Murayama, Phys. Rev. Lett. 111, 021601 (2013)

    Article  ADS  Google Scholar 

  42. T Brauner and M F Jakobsen, Phys. Rev. D 97, 025021 (2018)

    Article  ADS  Google Scholar 

  43. S Weinberg, Phys. Rev. Lett. 110, 241301 (2013)

    Article  ADS  Google Scholar 

  44. C Garcia-Cely, A Ibarra and E Molinaro, J. Cosmol. Astropart. Phys. 11, 061 (2013)

    Article  ADS  Google Scholar 

  45. M Frigerio, T Hambye and E Masso, Phys. Rev. X 1, 021026 (2011)

    Google Scholar 

  46. B Bellazzini, C Csaki, J Hubisz, J Shao and P Tanedo, J. High Energy Phys. 1109, 035 (2011)

    Article  ADS  Google Scholar 

  47. K Kannike and M Raidal, Phys. Rev. D 99, 115010 (2019)

    Article  ADS  Google Scholar 

  48. T Alanne, M Heikinheimo, V Keus, N Koivunen and K Tuominen, Phys. Rev. D 99, 075028 (2019)

    Article  ADS  Google Scholar 

  49. K Ghorbani and P Hossein Ghorbani, J. High Energy Phys. 1905, 096 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  50. K Ishiwata and T Toma, J. High Energy Phys. 1812, 089 (2018)

    Article  ADS  Google Scholar 

  51. A Arza, Eur. Phys. J. C 79, 250 (2019)

    Article  ADS  Google Scholar 

  52. R A El-Nabulsi, Can. J. Phys. 98, 130 (2019)

    Article  ADS  Google Scholar 

  53. S Kouwn, P Oh and C G Park, Phys. Rev. D 93, 083012 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  54. D Hadjimichef, AIP Conf. Proc. 1693, 050012 (2015)

    Google Scholar 

  55. R A El-Nabulsi, J. Magn. Magn. Mater. 458, 213 (2018)

    Article  ADS  Google Scholar 

  56. D Griffiths, Introduction to elementary particles (Wiley and Sons, 1987)

  57. S Dawson, Introduction to the physics of the Higgs bosons, Lectures given at the 1994 Theoretical Advanced Study Institute, Boulder, CO., May 30–June 23 (1994)

  58. M Krause, Higher-order corrections in the 2HDM, N2HDM and NMSSM, Ph.D. Thesis (von der KIT-Fakultät für Physik des Karlsruher Instituts für Technologie (KIT), 2019)

  59. Th N Duo, L Fritz, M Krause, M Mühlleitner and S Patel, Eur. Phys. J. C 80, 292 (2020)

    Article  ADS  Google Scholar 

  60. B Di Micco et al, Res. Phys. 5, 100045 (2020)

    Google Scholar 

  61. J R Espinosa, D Racco and A Riotto, J. Cosmol. Astropart. Phys. 09, 012 (2018)

    Article  ADS  Google Scholar 

  62. Y Hamada, H Kawai and K Y Oda, J. High Energy Phys. 07, 026 (2014)

    Article  ADS  Google Scholar 

  63. R A El-Nabulsi, Phys. Lett. B 619, 26 (2005)

    Article  ADS  Google Scholar 

  64. R A El-Nabulsi, Chin. Phys. Lett. 23, 1124 (2006)

    Article  Google Scholar 

  65. N Tetradis, J. Cosmol. Astropart. Phys. 09, 036 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  66. R A El-Nabulsi, Ind. J. Phys. 87, 465 (2013)

    Article  Google Scholar 

  67. R A El-Nabulsi, Chaos Solitons Fractals 41, 2262 (2009)

    Article  ADS  Google Scholar 

  68. P Huang, A J Long and L T Wang, Phys. Rev. D 94, 075008 (2016)

    Article  ADS  Google Scholar 

  69. P N Haba, K Kaneta and R Takahashi, J. High Energy Phys. 04, 029 (2014)

    Article  ADS  Google Scholar 

  70. S D Bass, A De Roeck and M Kado, Nat. Rev. Phys. (2021), https://doi.org/10.1038/s42254-021-00341-2

    Article  Google Scholar 

  71. R A El-Nabulsi, Commun. Theor. Phys. 54, 16 (2010)

    Article  ADS  Google Scholar 

  72. E J Copeland, Ann. Phys. 528, 62 (2016)

    Article  MathSciNet  Google Scholar 

  73. X Zhao, Proving the Higgs potential at current and future colliders, Ph.D. Thesis (UC Lovain, Institut de Recherche en Mathematique et Physique, 2020), http://hdl.handle.net/2078.1/240619

Download references

Acknowledgements

The authors would like to thank the referee for the careful reading and insightful remarks and suggestions which improved the paper.

Author information

Authors and Affiliations

  1. Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi & Waranont Anukool

  2. Quantum-Atom Optics Laboratory and Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi & Waranont Anukool

  3. Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Rami Ahmad El-Nabulsi & Waranont Anukool

Authors
  1. Rami Ahmad El-Nabulsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Waranont Anukool
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rami Ahmad El-Nabulsi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El-Nabulsi, R.A., Anukool, W. Spontaneous symmetry breaking and massive photons from a Fresnel-type potential. Pramana - J Phys 96, 186 (2022). https://doi.org/10.1007/s12043-022-02440-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-022-02440-w

Keywords

PACS No

Search

Navigation