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Grand Unification

-. Grand Unification. of the. strong. weak. and. electromagnetic. interactions. Standard Model. SU(3) x SU(2) x U(1). how to go beyond?. Leptons as a fourth color?. ( Pati-Salam - 1974 ). lepton number as fourth color?. SU(3) x SU(2) x U(1).

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Grand Unification

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  1. - Grand Unification of the strong weak and electromagnetic interactions

  2. Standard Model SU(3) x SU(2) x U(1) how to go beyond?

  3. Leptons as a fourth color? ( Pati-Salam - 1974 ) lepton number as fourth color? SU(3) x SU(2) x U(1) < SU (4) x SU (2, L) x SU (2, R)

  4. ( ( SU(4)

  5. (Q,L): (4,2,1) - - c c (Q,L): (4,1,2)

  6. ( ( =(4,2,1) ... required: righthanded partner of SM neutrino new "righthanded" W-bosons

  7. SU(4) ==> SU(3) x (B-L)

  8. - SU(3) x SU(2) x U(1) simple group

  9. simplest examples: SU(3)xSU(2)xU(1) < SU(5) (Georgi, Glashow, 1974) SU(3)xSU(2)xU(1) < SO(10) (Fritzsch, Minkowski, 1975 )

  10. SU(5) - theory: SU(3) x SU(2) x U(1) < SU(5) fermions of one family in two different representations:

  11. | sum of electric charges = 0

  12. Gauge bosons in SU(5) > SU(2) x U(1):adjoint representation ~ (24)5 x 5* = 24 + 124 = (8,1) + (1,3) + (1,1) + (3,2) + (3*,2) - - - - -

  13. - 24 = 12 gauge bosons: 8 gluons, 2 W-bosons, one Z boson, one photon + 12 superheavy color triplet gauge bosons

  14. Grand unification takes placeabove a very high unified mass scale M.Above this energy there is only one unified coupling constant g. The coupling constants for QCD and for the SU(2) x U(1) theory are the same, apart from Clebsch-Gordan coefficients.

  15. The rather different values of the three coupling constants at low energies are due to renormalization effects.

  16. - convergence of the coupling constants - grand unification -

  17. No convergence of coupling constants LEP data in SU(5)

  18. no convergence of the coupling constants

  19. convergence in case ofsupersymmetry (energy scale of supersymmetry: ~ 1000 GeV

  20. convergence of the coupling constants - SUSY

  21. Grand unification SU(3)xSU(2)xU(1) ==>SO(10) ( Fritzsch - Minkowski; Georgi - 1975 )

  22. SU(3) x SU(2) x U(1)< SU(4) x SU(2,L) x SU(2,R)~ SO(6) x SO(4)=> SO(10)

  23. Representations of SO(10):16-dimensional spinor representation( => Pauli spinor ~ SO(3) )

  24. 16: SO(10)

  25. ) ) 16 =

  26. SO(10) SO(6) x SO(4) _ SU(4) x SU(2,L) x SU(2,R) _ SU(3) x SU(2,L) x U(1) _

  27. SO(10):due to the two intermediate energy scales there is no problem with the convergence of the coupling constants at the grand unified mass scale

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