Yang--Mills duality as origin of generations, quark mixing and neutrino oscillations

Abstract

The origin of fermion generations is one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of electric-magnetic duality. First, nonabelian duality says that dual to the colour (electric) symmetry SU(3), there is a ``colour magnetic symmetry'' $\widetilde{SU}(3)$, which by a result of 't~Hooft is spontaneously broken and can thus play the role of the "horizontal symmetry" of generations. Second, nonabelian duality suggests the manner this symmetry is broken with frame vectors in internal symmetry space acting as Higgs fields. As a result, mass matrices factorize leading to fermion mass hierarchy. A calculation to first order gives mixing (CKM and MNS) matrices in general agreement with experiment. In particular, quark mixing is seen naturally to be weak compared with leptons, while within the lepton sector, $\mu-\tau$ mixing turns out near maximal but $e-\tau$ mixing small, just as seen in recent $\nu$ oscillation experiments. In addition, the scheme leads to many testable predictions ranging from rare FCNC meson decays and $\mu-e$ conversion in nuclei to cosmic ray air showers above $10^{20}$ eV.