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Journal of High Energy Physics

, 2015:11 | Cite as

Grand unification in the spectral Pati-Salam model

  • Ali H. Chamseddine
  • Alain Connes
  • Walter D. van SuijlekomEmail author
Open Access
Regular Article - Theoretical Physics
First Online:

Abstract

We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different scenarios for the scalar particle content which are determined by the precise form of the Dirac operator for the finite noncommutative space. We consider these different scenarios and establish for all of them unification of the Pati-Salam gauge couplings. The boundary conditions are set by the usual RG flow for the Standard Model couplings at an intermediate mass scale at which the Pati-Salam symmetry is broken.

Keywords

Beyond Standard Model Non-Commutative Geometry Spontaneous Symmetry Breaking Renormalization Group 
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Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].ADSGoogle Scholar
  2. [2]
    U. Aydemir, D. Minic, C. Sun and T. Takeuchi, Pati-Salam unification from non-commutative geometry and the TeV-scale W R boson, arXiv:1509.01606 [INSPIRE].
  3. [3]
    V.D. Barger, E. Ma and K. Whisnant, General analysis of a possible second weak neutral current in gauge models, Phys. Rev. D 26 (1982) 2378 [INSPIRE].ADSGoogle Scholar
  4. [4]
    A.H. Chamseddine and A. Connes, Universal formula for noncommutative geometry actions: unification of gravity and the Standard Model, Phys. Rev. Lett. 77 (1996) 4868 [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  5. [5]
    A.H. Chamseddine and A. Connes, The spectral action principle, Commun. Math. Phys. 186 (1997) 731 [hep-th/9606001] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  6. [6]
    A.H. Chamseddine and A. Connes, Why the Standard Model, J. Geom. Phys. 58 (2008) 38 [arXiv:0706.3688] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  7. [7]
    A.H. Chamseddine and A. Connes, Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I, Fortsch. Phys. 58 (2010) 553 [arXiv:1004.0464] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  8. [8]
    A.H. Chamseddine and A. Connes, Resilience of the spectral Standard Model, JHEP 09 (2012) 104 [arXiv:1208.1030] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  9. [9]
    A.H. Chamseddine, A. Connes and M. Marcolli, Gravity and the Standard Model with neutrino mixing, Adv. Theor. Math. Phys. 11 (2007) 991 [hep-th/0610241] [INSPIRE].zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    A.H. Chamseddine, A. Connes and V. Mukhanov, Geometry and the quantum: basics, JHEP 12 (2014) 098 [arXiv:1411.0977] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  11. [11]
    A.H. Chamseddine, A. Connes and V. Mukhanov, Quanta of geometry: noncommutative aspects, Phys. Rev. Lett. 114 (2015) 091302 [arXiv:1409.2471] [INSPIRE].CrossRefADSGoogle Scholar
  12. [12]
    A.H. Chamseddine, A. Connes and W.D. van Suijlekom, Beyond the spectral Standard Model: emergence of Pati-Salam unification, JHEP 11 (2013) 132 [arXiv:1304.8050] [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    D. Chang, R.N. Mohapatra and M.K. Parida, A new approach to left-right symmetry breaking in unified gauge theories, Phys. Rev. D 30 (1984) 1052 [INSPIRE].ADSGoogle Scholar
  14. [14]
    T.P. Cheng, E. Eichten and L.-F. Li, Higgs phenomena in asymptotically free gauge theories, Phys. Rev. D 9 (1974) 2259 [INSPIRE].ADSGoogle Scholar
  15. [15]
    V. Elias, Coupling constant renormalization in unified gauge theories containing the Pati-Salam model, Phys. Rev. D 14 (1976) 1896 [INSPIRE].ADSGoogle Scholar
  16. [16]
    V. Elias, Gauge coupling constant magnitudes in the Pati-Salam model, Phys. Rev. D 16 (1977) 1586 [INSPIRE].ADSGoogle Scholar
  17. [17]
    M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].CrossRefADSGoogle Scholar
  19. [19]
    M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, Nucl. Phys. B 249 (1985) 70 [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    W. McKay and J. Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lect. Notes Pure Appl. Math. 69, Marcel Dekker Inc., New York U.S.A. (1981).Google Scholar
  21. [21]
    R. Mohapatra, Unification and supersymmetry. The frontiers of quark-lepton physics, third edition, Springer, New York U.S.A. (2003).Google Scholar
  22. [22]
    J.C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Ali H. Chamseddine
    • 1
    • 2
  • Alain Connes
    • 2
    • 3
    • 4
  • Walter D. van Suijlekom
    • 5
    Email author
  1. 1.Physics DepartmentAmerican University of BeirutBeirutLebanon
  2. 2.College de FranceParisFrance
  3. 3.I.H.E.S.Bures-sur-YvetteFrance
  4. 4.Department of MathematicsThe Ohio State UniversityColumbusU.S.A.
  5. 5.Institute for MathematicsAstrophysics and Particle Physics, Radboud University NijmegenNijmegenThe Netherlands

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