The origin of fermion families and the value of the fine structure constant

英文摘要：

This paper is concerned with a way of thinking about the standard model that explains the existence of three fermion families and the value of the fine structure constant. The main idea is that the ultraviolet divergences that we encounter in the quantum field theories of the standard model, when interpreted appropriately, have a deep physical significance that leads to new relationships between the physical and bare masses quarks and leptons. This interpretation is based on the assumption of a quantum gravity induced ultraviolet cutoff at the Planck scale and a novel approach to mass renormalization in which the usual perturbation series for the self-mass of a quark or lepton is rearranged and formally summed. Perturbing around the formally summed expression leads to self-consistency equations for the physical quark and lepton masses with multiple solutions that lie outside the reach of conventional perturbation theory. When applied to the standard model at the lowest level of approximation, this approach explains how three generations of charged leptons with a mass spectrum and a value of the fine structure constant in rough agreement with experiment can emerge from a universal bare mass and bare electromagnetic charge. This approach also explains how three generations of physical quark doublets (six flavors) can emerge from a universal bare doublet and bare color charge. Finally, it explains the origin of mixing (and CP violation) and the absence of flavor-changing neutral currents.