Are preons dyons? Naturalness of three generations

Abstract

In the present paper a model of preons and their composites is constructed in the framework of the superstring-inspired `flipped' E_6\times \widetilde{E_6} gauge symmetry group which reveals a generalized dual symmetry. Here E_6 and \widetilde{E_6} are non-dual and dual sectors of the theory with hyper-electric g and hyper-magnetic \tilde g charges, respectively. We follow the old idea by J. Pati presuming that preons are dyons, which in our model are confined by hyper-magnetic strings -- composite {\bf N}=1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. Considering preons belonging to the 27-plet of E_6, we have investigated the breakdown of E_6 (and \widetilde{E_6}) near the Planck scale into the SU(6)\times U(1) (and \widetilde{SU(6)}\times \widetilde{U(1)}) gauge group and shown that the six types of strings having fluxes \Phi_n=n\Phi_0 (n=\pm 1,\pm 2,\pm 3) produce three (and only three) generations of composite quark-leptons and bosons. The model predicts the existence of the Family replicated gauge group [E_6]^3 near the Planck scale. The runnings of the corresponding fine structure constants are investigated, and the critical coupling constants at the two phase transition points near the Planck scale are calculated. The model explains the hierarchies of masses in the Standard Model naturally. The compactification in a space-time with five dimensions and its influence on form-factors of composite objects are also briefly discussed.