Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 012, 15 pages      arXiv:0707.4551      http://dx.doi.org/10.3842/SIGMA.2008.012
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Preon Model and Family Replicated E6 Unification

Chitta Ranjan Das a and Larisa V. Laperashvili b
a) The Institute of Mathematical Sciences, Chennai, India
b) The Institute of Theoretical and Experimental Physics, Moscow, Russia

Received October 02, 2007, in final form January 24, 2008; Published online February 02, 2008

Abstract
Previously we suggested a new preon model of composite quark-leptons and bosons with the 'flipped' E6 × ˜E6 gauge symmetry group. We assumed that preons are dyons having both hyper-electric g and hyper-magnetic ˜g charges, and these preons-dyons are confined by hyper-magnetic strings which are an N = 1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. In the present paper we show that the existence of the three types of strings with tensions Tk = kT0 (k = 1,2,3) producing three (and only three) generations of composite quark-leptons, also provides three generations of composite gauge bosons ('hyper-gluons') and, as a consequence, predicts the family replicated [E6]3 unification at the scale ~1017 GeV. This group of unification has the possibility of breaking to the group of symmetry: [SU(3)C]3 × [SU(2)L]3 × [U(1)Y]3 × [U(1)(B-L)]3 which undergoes the breakdown to the Standard Model at lower energies. Some predictive advantages of the family replicated gauge groups of symmetry are briefly discussed.

Key words: preon; dyon; monopole; unification; E6.

pdf (425 kb)   ps (331 kb)   tex (256 kb)

References

  1. Wilczek F., Zee A., Horizontal interaction and weak mixing angles, Phys. Rev. Lett. 42 (1979), 421-425.
  2. Bennett D.L., Nielsen H.B., Picek I., Understanding fine structure constants and three generations, Phys. Lett. B 208 (1988), 275-280.
  3. Froggatt C.D., Nielsen H.B., Origin of symmetries, Singapore, World Scientific, 1991.
  4. Laperashvili L.V., The standard model and the fine structure constant at Planck distances in Bennet-Brene-Nielsen-Picek random dynamics, Yad. Fiz. 57 (1994), 501-508 (English transl.: Phys. Atom. Nucl. 57 (1994), 471-478).
  5. Nielsen H.B., Takanishi Y., Neutrino mass matrix in anti-GUT with seesaw mechanism, Nuclear Phys. B 604 (2001), 405-425, hep-ph/0011062.
  6. Nielsen H.B., Takanishi Y., Baryogenesis via lepton number violation in anti-GUT model, Phys. Lett. B 507 (2001), 241-251, hep-ph/0101307.
  7. Froggatt C.D., Nielsen H.B., Takanishi Y., Family replicated gauge groups and large mixing angle solar neutrino solution, Nuclaer Phys. B 631 (2002), 285-306, hep-ph/0201152.
  8. Froggatt C.D., Laperashvili L.V., Nielsen H.B., Takanishi Y., Family replicated gauge group models, in Proceedings of Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" (June 23-29, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Proceedings of Institute of Mathematics, Kyiv 50 (2004), Part 2, 737-743, hep-ph/0309129.
  9. Bennett D.L., Nielsen H.B., Prediction for nonabelian fine structure constants from multicriticality, Internat. J. Modern Phys. A 9 (1994), 5155-5200, hep-ph/9311321.
  10. Froggatt C.D., Nielsen H.B., Standard model criticality prediction: top mass 1735 GeV and Higgs mass 135 9 GeV, Phys. Lett. B 368 (1996), 96-102, hep-ph/9511371.
  11. Froggatt C.D., Laperashvili L.V., Nielsen H.B., The fundamental-weak scale hierarchy in the standard model, Phys. Atom. Nucl. 69 (2006), 67-80, hep-ph/0407102.
  12. Das C.R., Laperashvili L.V., Phase transition in gauge theories, monopoles and the multiple point principle, Internat. J. Modern Phys. A 20 (2005), 5911-5988, hep-ph/0503138.
  13. Froggatt C.D., Nielsen H.B., Trying to understand the standard model parameters, Invited talk by H.B. Nielsen at the "XXXI ITEP Winter School of Physics" (February 18-26, 2003, Moscow, Russia), Surveys High Energy Phys. 18 (2003), 55-75, hep-ph/0308144.
  14. Das C.R., Laperashvili L.V., Are preons dyons? Naturalness of three generations, Phys. Rev. D 74 (2006), 035007, 12 pages, hep-ph/0605161.
  15. Das C.R., Laperashvili L.V., Composite model of quark-leptons and duality, hep-ph/0606042.
  16. Laperashvili L.V., Das C.R., Dyons near the Planck scale, Internat. J. Modern Phys. A 22 (2007), 5211-5228, hep-ph/0606043.
  17. Green M.B., Schwarz J.H., Witten E., Superstring theory, Vol. 1, 2, Cambridge University Press, Cambridge, 1988.
  18. Green M.B., Schwarz J.H., Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984), 117-122.
  19. Green M.B., Schwarz J.H., Infinity cancellations in SO(32) superstring theory, Phys. Lett. B 151 (1985), 21-25.
  20. Gross D.J., Harvey J.A., Martinec E., Rohm R., The heterotic string, Phys. Rev. Lett. 54 (1985), 502-505.
  21. Gross D.J., Harvey J.A., Martinec E., Rohm R., Heterotic string theory. 1. The free heterotic string, Nuclear Phys. B 256 (1985), 253-284.
  22. Gross D.J., Harvey J.A., Martinec E., Rohm R., Heterotic string theory. 2. The interacting heterotic string, Nuclear Phys. B 267 (1986), 75-124.
  23. Pati J.C., Magnetism as the origin of preon binding, Phys. Lett. B 98 (1981), 40-44.
  24. Pati J.C., Salam A., Strathdee J., A preon model with hidden electric and magnetic type charges, Nuclear Phys. B 185 (1981), 416-428.
  25. Marshakov A., Yung A., Non-Abelian confinement via Abelian flux tubes in softly broken N = 2 SUSY QCD, Nuclear Phys. B 647 (2002), 3-48, hep-th/0202172.
  26. Markov V., Marshakov A., Yung A., Non-Abelian vortices in N = 1* gauge theory, Nucl. Phys. B 709 (2005), 267-295, hep-th/0408235.
  27. Gorsky A., Shifman M.,Yung A., Non-Abelian Meissner effect in Yang-Mills theories at weak coupling, Phys. Rev. D 71 (2005), 045010, 16 pages, hep-th/0412082.
  28. Shifman M., Yung A., Non-Abelian flux tubes in SQCD: supersizing world-sheet supersymmetry, Phys. Rev. D 72 (2005), 085017, 19 pages, hep-th/0501211.
  29. Auzzi R., Shifman M., Yung A., Composite non-Abelian flux tubes in N = 2 SQCD, Phys. Rev. D 73 (2006), 105012, 15 pages, Erratum, Phys. Rev. D 76 (2007), 109901, 3 pages, hep-th/0511150.
  30. Chaichian M., Chkareuli J.L., Kobakhidze A., Composite quarks and leptons in higher space-time dimensions, Phys. Rev. D 66 (2002), 095013, 7 pages, hep-ph/0108131.
  31. Abrikosov A.A., On the magnetic properties of superconductors of the second group, Zh. Eksp. Teor. Fiz. 32 (1957), 1442-1452 (English transl.: Sov. Phys. JETP 5 (1957), 1174-1182).
  32. Nielsen H.B., Olesen P., Vortex line models for dual strings, Nuclear Phys. B 61 (1973), 45-61.
  33. Cecotti S., Derendinger J.P., Ferrara S., Girardello L., Properties of E6 breaking and superstring theory, Phys. Lett. B 156 (1985), 318-326.
  34. Das C.R., Laperashvili L.V., Seesaw scales and the steps from the standard model towards superstring-inspired flipped E6, hep-ph/0604052.
  35. Pati J.C., Salam A., Lepton number as the fourth color, Phys. Rev. D 10 (1974), 275-289, Erratum, Phys. Rev. D 11 (1975), 703-703.
  36. Mohapatra R.N., Pati J.C., Left-right gauge symmetry and an isoconjugate model of CP violation, Phys. Rev. D 11 (1975), 566-571.
  37. Mohapatra R.N., Pati J.C., A natural left-right symmetry, Phys. Rev. D 11 (1975), 2558-2561.
  38. Kovalenko P.A., Laperashvili L.V., The effective QCD Lagrangian and renormalization group approach, Yad. Fiz. 62 (1999), 1857-1867 (English transl.: Phys. Atom. Nucl. 62 (1999), 1729-1738), hep-ph/9711390.
  39. Matinyan S.G., Savvidy G.K., Vacuum polarization induced by the intense gauge field, Nuclear Phys. B 134 (1978), 539-545.
  40. Matinyan S.G., Savvidy G.K., On the radiative corrections to classical Lagrangian and dynamical symmetry breaking, Yad. Fiz. 25 (1977), 218-226.
  41. Batalin I.A., Matinyan S.G., Savvidy G.K., Vacuum polarization by a source-free gauge field, Yad. Fiz. 26 (1977), 407-414 (English transl.: Sov. J. Nucl. Phys. 26 (1977), 214-217).
  42. Nielsen H.B., Olesen P., A quantum liquid model for the QCD vacuum gauge and rotational invariance of domained and quantized homogeneous color fields, Nuclear Phys. B 160 (1979), 380-396.
  43. Bennett D.L., Laperashvili L.V., Nielsen H.B., Relation between finestructure constants at the Planck scale from multiple point principle, in Proceedings of the 9th Workshop on "What Comes Beyond the Standard Model" (September 16-26, 2006, Bled, Slovenia), Editors S. Ansoldi et al., DMFA-Zaloznistvo, Ljubljana, Slovenia (2006), 10-24, hep-ph/0612250.
  44. Bennett D.L., Laperashvili L.V., Nielsen H.B., Finestructure constants at the Planck scale from multiple point principle, in Proceedings of the 10th Workshop on "What Comes Beyond the Standard Model" (July 17-27, 2007, Bled, Slovenia), Editors N. Mankoc Borstnik et al., DMFA-Zaloznistvo, Ljubljana, Slovenia 8 (2007), no. 2, 1-30, arXiv:0711.4681.
  45. Yao W.-M. et al. (Particle Data Group), Review of particle physics, J. Phys. G 33 (2006), 1-1232.
  46. Laperashvili L.V., Nielsen H.B., The problem of monopoles in the standard and family replicated models, in Proceedings of the 11th "Lomonosov Conference on Elementary Particle Physics" (August 21-27, 2003, Moscow, Russia), "Moscow 2003, Particle Physics in Laboratory, Space and Universe", 2003, 331-337, hep-th/0311261.
  47. Laperashvili L.V., Nielsen H.B., Ryzhikh D.A., Monopoles and family replicated unification, Yad. Fiz. 66 (2003), 2119-2127 (English transl.: Phys. Atom. Nucl. 66 (2003), 2070-2077), hep-th/0212213.

Previous article   Next article   Contents of Volume 4 (2008)