Determining fermion masses and resolving the problem of generations: A clue to incorporate Gravity into the Standard Model

Abstract

Inspired by the Poincare model of the electron, elementary fermions are assumed to be bubble like structures with negative internal pressure and a size corresponding to a radius or equivalently an ultraviolet cut-off. Negative pressure, self-interaction of gauge fields up to the cut-off energy and gravity contribute to the self-energy. All corrections are considered to be proportional to the observed mass of the fermion in order to preserve chiral symmetry in the limit of vanishing fermion mass. Fermion self-energy is thus constituted of terms; inverse cubic, logarithmic (as in qed self-energy of the electron), linear and quadratic in the cut-off parameter and defines coupling coefficients. The latter two terms originating from gravity are fixed on basis of dimensional considerations. The condition of extremization of total energy to determine equilibrium states, leads to a quantic equations with three real roots, giving three values for the fermion mass, for each set of coupling coefficients. The model represents observed quark – lepton mass ratios explaining generation problem and suggest possible numerical values for neutrino masses in agreement with the oscillation data in an inverted order. As a result of incorporation of gravity, Planck energy sets as the natural physically meaningful scale, deriving other scales corresponding to sizes of elementary fermions ranging from Planck length to few thousand times this unit. The model interprets, the physical quality distinguishing a generation as the phase of the false vacuum ‘inside’ the elementary bubble. The unconventional approach behind the model may also have implications on unifications of couplings, incorporation of gravity into the standard model and issue of divergences in quantum field theories.