keeping both the axial and electric charges conserved automatically keeps the
proton stable. We however find that we need to double the number of quarks,
this may seem a step backwards (but see later). Why double the number of quarks? Well our axial force has opposite charge on the left and right handed particles, which means the have either transform to something else when you overtake them, or keep the same spin. But Protons and Neutrons seem to reflect they spins just fine. Then in order to let the quarks keep the same charge under
reflection, we need a another pair of heavier quarks per generation that they can
transform to thus we get.
field. By mixing the particles we arrive at mass states with the same axial charge
on both the right and left handed particles. Adding these heavy tera-quark states, turns the 15 particles for one generation of the standard model, in a group of 27
particles. One 27 particle group, is the fundamental representations of the
exceptional group E6. Let arrange the particles as below. [Warning wide browser required]
that is it can break left-right symmetry, in the above only a left handed weak force
should be present. Two copies of E6 and two the right handed neutrinos, make up the non
chiral group E7.
E7 ~ E6 + (anti E6) + (1) + (anti 1).
But even better three generations of E6's and the antiparticles fit exactly into String theorys favourite
group E8.
E8 ~ (8) + (78, E6 adjoint) + 3*(E6) + 3*(anti E6).
The E6 adjoint gives (under supersymmetry) the forces acting universally on each generation.
The right handed neutrinos needed for the axial force, are missing and presummably fall into the remaining
8 particles, which permute the generation number, as below.
this model. We also predict one extra right handed neutrino, that doesn't feel the axial force. And we seem to predict tri-bimaxially neutrino mixing. However there is no room for Higgs bosons in it. The Higgs will have to be composite particles builts from interactions between some of the above fermions. Some chiral condensate needs to form to give the particles mass. It should be noted that all this is speculation not yet backed up by any concrete math.
