Advertisement

Phenomenology of the Noncommutative Standard Model

  • Walter D. van SuijlekomEmail author
Chapter
  • 1.5k Downloads
Part of the Mathematical Physics Studies book series (MPST)

Abstract

>In Theorems  11.10 and  11.11, we have derived the full Lagrangian for the Standard Model from the almost-commutative manifold \(M\times F_{\scriptscriptstyle SM}\).

Keywords

Higgs Boson Renormalization Group Yukawa Coupling Higgs Mass Noncommutative Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Chamseddine, A.H., Connes, A., Marcolli, M.: Gravity and the standard model with neutrino mixing. Adv. Theory Math. Phys. 11, 991–1089 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Connes, A., Marcolli, M.: Noncommutative Geometry. Quantum Fields and Motives. AMS, Providence (2008)Google Scholar
  3. 3.
    Jureit, J., Krajewski, T., Schücker, T., Stephan, C.A.: Seesaw and noncommutative geometry. Phys. Lett. B 654, 127–132 (2007)CrossRefzbMATHMathSciNetADSGoogle Scholar
  4. 4.
    van den Dungen, K., van Suijlekom, W.D.: Particle physics from almost commutative spacetimes. Rev. Math. Phys. 24, 1230004 (2012)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Mohapatra, R., Pal, P.: Massive neutrinos in physics and astrophysics, 2nd edn. World Sci. Lect. Notes Phys. 60, 1–397 (1998)Google Scholar
  6. 6.
    Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (i) wave function renormalization. Nucl. Phys. B 222, 83–103 (1983)CrossRefADSGoogle Scholar
  7. 7.
    Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (ii) Yukawa couplings. Nucl. Phys. B 236, 221–232 (1984)CrossRefADSGoogle Scholar
  8. 8.
    Machacek, M., Vaughn, M.: Two-loop renormalization group equations in a general quantum field theory: (iii) Scalar quartic couplings. Nucl. Phys. B 249, 70–92 (1985)CrossRefADSGoogle Scholar
  9. 9.
    Ford, C., Jones, D.R.T., Stephenson, P.W., Einhorn, M.B.: The effective potential and the renormalisation group. Nucl. Phys. B 395, 17–34 (1993)CrossRefADSGoogle Scholar
  10. 10.
    Nakamura, K., et al.: Review of particle physics. J. Phys. G: Nucl. Part. Phys. 37, 075021 (2010)CrossRefADSGoogle Scholar
  11. 11.
    Appelquist, T., Carazzone, J.: Infrared singularities and massive fields. Phys. Rev. D 11, 2856–2861 (1975)CrossRefADSGoogle Scholar
  12. 12.
    Antusch, S., Kersten, J., Lindner, M., Ratz, M.: Neutrino mass matrix running for non-degenerate see-saw scales. Phys. Lett. B 538, 87–95 (2002)CrossRefADSGoogle Scholar
  13. 13.
    Aad, G., et al.: Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B716, 1–29 (2012)CrossRefADSGoogle Scholar
  14. 14.
    Chatrchyan, S., et al.: Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B716, 30–61 (2012)CrossRefADSGoogle Scholar
  15. 15.
    Essouabri, D., Iochum, B., Levy, C., Sitarz, A.: Spectral action on noncommutative torus. J. Noncommut. Geom. 2, 53–123 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Gayral, V., Lochum, B.: The spectral action for Moyal planes. J. Math. Phys. 46(043503), 17 (2005)Google Scholar
  17. 17.
    Grosse, H., Wulkenhaar, R.: 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory. J. Geom. Phys. 62, 1583–1599 (2012)CrossRefzbMATHMathSciNetADSGoogle Scholar
  18. 18.
    Iochum, B., Levy, C., Sitarz, A.: Spectral action on \(SU_q(2)\). Commun. Math. Phys. 289, 107–155 (2009)CrossRefzbMATHMathSciNetADSGoogle Scholar
  19. 19.
    Eckstein, M., Lochum, B., Sitarz, A.: Heat trace and spectral action on the standard Podles sphere. Commun. Math. Phys. (published online: 6 May 2014)Google Scholar
  20. 20.
    Farnsworth, S., Boyle, L.: Non-associative geometry and the spectral action principle. arXiv:1303.1782
  21. 21.
    Boyle, L., Farnsworth, S.: Non-commutative geometry, non-associative geometry and the standard model of particle, physics. arXiv:1401.5083
  22. 22.
    Chamseddine, A.H., Connes, A.: Universal formula for noncommutative geometry actions: unifications of gravity and the standard model. Phys. Rev. Lett. 77, 4868–4871 (1996)CrossRefzbMATHMathSciNetADSGoogle Scholar
  23. 23.
    Wilson, K.G.: Renormalization group methods. Adv. Math. 16, 170–186 (1975)CrossRefGoogle Scholar
  24. 24.
    Iochum, B., Levy, C., Vassilevich, D.: Spectral action beyond the weak-field approximation. Commun. Math. Phys. 316, 595–613 (2012)CrossRefzbMATHMathSciNetADSGoogle Scholar
  25. 25.
    Iochum, B., Levy, C., Vassilevich, D.: Global and local aspects of spectral actions. J. Phys. A45, 374020 (2012)MathSciNetGoogle Scholar
  26. 26.
    Kurkov, M., Lizzi, F., Vassilevich, D.: High energy bosons do not propagate. Phys. Lett. B731, 311–315 (2014)Google Scholar
  27. 27.
    van Suijlekom, W.D.: Renormalization of the spectral action for the Yang-Mills system. JHEP 1103, 146 (2011)CrossRefADSGoogle Scholar
  28. 28.
    van Suijlekom, W.D.: Renormalization of the asymptotically expanded Yang-Mills spectral action. Commun. Math. Phys. 312, 883–912 (2012)CrossRefzbMATHADSGoogle Scholar
  29. 29.
    van Suijlekom, W.D.: Renormalizability conditions for almost commutative manifolds. Ann. H. Poincaré 15, 985–1011 (2014)Google Scholar
  30. 30.
    van Suijlekom, W.D.: Renormalizability conditions for almost-commutative geometries. Phys. Lett. B711, 434–438 (2012)CrossRefADSGoogle Scholar
  31. 31.
    Stephan, C.A.: Almost-commutative geometries beyond the standard model. J. Phys. A39, 9657 (2006)ADSGoogle Scholar
  32. 32.
    Stephan, C.A.: Almost-commutative geometries beyond the Standard Model. ii. new colours. J. Phys. A40, 9941 (2007)ADSGoogle Scholar
  33. 33.
    Stephan, C.A.: New scalar fields in noncommutative geometry. Phys. Rev. D79, 065013 (2009)ADSGoogle Scholar
  34. 34.
    Stephan, C.A.: Beyond the standard model: a noncommutative approach. arXiv:0905.0997
  35. 35.
    Stephan, C.A.: A dark sector extension of the almost-commutative standard model. Int. J. Mod. Phys. A29, 1450005 (2014)CrossRefADSGoogle Scholar
  36. 36.
    van den Broek, T., van Suijlekom, W.D.: Supersymmetric QCD and noncommutative geometry. Commun. Math. Phys. 303, 149–173 (2011)CrossRefzbMATHADSGoogle Scholar
  37. 37.
    van den Broek, T., van Suijlekom, W.D.: Supersymmetric QCD from noncommutative geometry. Phys. Lett. B699, 119–122 (2011)CrossRefADSGoogle Scholar
  38. 38.
    Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part I: supersymmetric almost-commutative geometries (to appear)Google Scholar
  39. 39.
    Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part II: supersymmetry breaking (to appear)Google Scholar
  40. 40.
    Beenakker, W., van den Broek, T., van Suijlekom, W.: Noncommutative and supersymmetry. Part III: the noncommutative supersymmetric standard model (to appear)Google Scholar
  41. 41.
    Estrada, C., Marcolli, M.: Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models. Int. J. Geom. Meth. Mod. Phys. 10, 1350036 (2013)CrossRefMathSciNetGoogle Scholar
  42. 42.
    Sher, M.: Electroweak Higgs potentials and vacuum stability. Phys. Rept. 179, 273–418 (1989)CrossRefADSGoogle Scholar
  43. 43.
    Chamseddine, A.H., Connes, A.: Resilience of the spectral standard model. JHEP 1209, 104 (2012)CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    Chamseddine, A.H., Connes, A.: Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I. Fortsch. Phys. 58, 553–600 (2010)CrossRefzbMATHMathSciNetADSGoogle Scholar
  45. 45.
    Ćaćić, B.: A reconstruction theorem for almost-commutative spectral triples. Lett. Math. Phys. 100, 181–202 (2012)CrossRefzbMATHMathSciNetADSGoogle Scholar
  46. 46.
    Ćaćić, B.: Real structures on almost-commutative spectral triples. Lett. Math. Phys. 103, 793–816 (2013)CrossRefzbMATHMathSciNetADSGoogle Scholar
  47. 47.
    Boeijink, J., van den Dungen, K.: Notes on topologically non-trivial almost-commutative geometries. arXiv:1405.5368
  48. 48.
    Pati, J.C., Salam, A.: Lepton number as the fourth color. Phys. Rev. D10, 275–289 (1974)ADSGoogle Scholar
  49. 49.
    Chamseddine, A.H., Connes, A., Van Suijlekom, W.D.: Inner fluctuations in noncommutative geometry without the first order condition. J. Geom. Phys. 73, 222–234 (2013)CrossRefzbMATHMathSciNetADSGoogle Scholar
  50. 50.
    Chamseddine, A.H., Connes, A., van Suijlekom, W.D.: Beyond the spectral standard model: emergence of Pati-Salam unification. JHEP 1311, 132 (2013)CrossRefADSGoogle Scholar
  51. 51.
    Devastato, A., Lizzi, F., Martinetti, P.: Grand symmetry, spectral action, and the Higgs mass. JHEP 1401, 042 (2014)CrossRefADSGoogle Scholar
  52. 52.
    Chamseddine, A.H., Connes, A.: Why the standard model. J. Geom. Phys. 58, 38–47 (2008)CrossRefzbMATHMathSciNetADSGoogle Scholar
  53. 53.
    Gonderinger, M., Li, Y., Patel, H., Ramsey-Musolf, M.J.: Vacuum stability, perturbativity, and scalar singlet dark matter. JHEP 1001, 053 (2010)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.IMAPPRadboud University NijmegenNijmegenThe Netherlands

Personalised recommendations