Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions

Abstract: We provide theoretical evidence that the neutrino is a Majorana fermion. This evidence comes from assuming that the standard model and beyond-standard-model physics can be described through division algebras, coupled to a quantum dynamics. We use the division algebras scheme to derive mass ratios for the standard model charged fermions of three generations. The predicted ratios agree well with the observed values if the neutrino is assumed to be Majorana. However, the theoretically calculated ratios completely disagree with known values if the neutrino is taken to be a Dirac particle. Towards the end of the article we discuss prospects for unification of the standard model with gravitation if the assumed symmetry group of the theory is $E_6$, and if it is assumed that space-time is an 8D octonionic space-time, with 4D Minkowski space-time being an emergent approximation. Remarkably, we find evidence that the precursor of classical gravitation, described by the symmetry $SU(3){grav} \times SU(2)_R \times U(1){grav}$ is the right-handed counterpart of the standard model $SU(3)_{color} \times SU(2)_L \times U(1)_Y$.