The Charge Field and the Origin of Fermion Generations

AbstractWhy matter comes in three generations has so far been an unanswered question. This paper answers it. A single eigenstate equation, derived from first principles within the Charge Field framework, gives the masses of the higher-generation charged fermions. From the three ground-state masses and the muon alone, it predicts the other five: the tau, strange and bottom to within 6%, the charm to 5% and the top to 11%. The nine Yukawa couplings of the Standard Model reduce to three.The equation follows from the mechanism by which a fermion acquires its charge from the Charge Field (CF). Charge is acquired through the irreversible assimilation of a charge boson’s quantum at the fermion’s CF vertex, by the very potential, of the form 1/r⁴, that the quantum generates through its self-interaction. That same potential holds three possible eigenstate shells, in any one of which a fermion’s wavefunction can settle. Depending on which shell its wavefunction settles in, the same fermion is observed as one of its three generations. A heavier generation’s extra mass is not a larger Higgs coupling but the energy of its eigenstate, added to the Higgs rest mass of the ground eigenstate.Thus the binding potential is responsible for the three observed generations. It supports three deep bound states and a fourth, marginal one that never forms: three generations, and no fourth, as every collider search has found.For the neutrino sector, oscillation experiments measure only the differences between the squared masses of its three states; the masses themselves are still unknown. With a rest-floor mass of confinement that needs no new particle, and with one parameter fitted to the observed differences, the framework derives the masses of the three neutrino generations: m1 = 15.0 meV, m2 = 17.3 meV and m3 = 52.3 meV. Their sum, 84.6 meV, is a value forthcoming cosmological surveys can test.Some earlier proposals of higher generations as excited states were numerical patterns with no mechanism. This result rests on a derived potential, an eigenstate equation and an explicit dynamical mechanism: the same charge-acquisition event that accounts for the absence of antimatter (Paper 1). The threefold replication of matter emerges as a quantitative prediction of the Charge Field framework.