Why do elementary particles have such strange looking mass ratios?

The neutrino, down quark, up quark, and the electron have a simple electric charge ratio of (0, 1/3, 2/3, 1). Each of these four elementary particles have a second generation counterpart and a third generation counterpart having the same electric charge but different masses. For instance, the electron, the muon and the tau-lepton all have the same electric charge but a mass ratio approximately (1, 206, 3477). Similarly, the quarks also have strange looking mass ratios. What is the origin of these mysterious mass ratios, whereas the ratios of electric charges are so simple? We recall that the standard model of particle physics is a highly successful quantum field theory of the electroweak force and the strong force, whereas mass is not related to any of these forces but to gravitation. We have recently proposed a left-right symmetric extension of the standard model so as to include gravitation, where the symmetries derive from the algebra of a number system known as the octonions. The theory also yields a simple mathematical derivation of the above-mentioned strange looking mass ratios of quarks and charged leptons. In this colloquium we will give an elementary account of these recent findings, and show that the mass ratios are also simple fractions, analogous to the ratios of electric charges.

Reference:

1. Majorana neutrinos, exceptional Jordan algebra, and mass ratios of charged fermions
    Vivan Bhatt (IIT Madras), Rajrupa Mondal (IISER Kolkata), Vatsalya Vaibhav (IIT Kanpur)  and T. P. Singh
    Journal of Physics G: Nuclear and Particle Physics (in press)
     https://iopscience.iop.org/article/10.1088/1361-6471/ac4c91
     https://arxiv.org/abs/2108.05787v2 [hep-ph]