A Semiclassical Model of Leptons

Abstract

A semi-classical model of leptons is presented on the assumption that they are stable equilibrium states of spherical bubble like extended structures with negative pressure of a false vacuum created inside and balanced by an outward stress due to vacuum polarization originating from the charge residing on the surface. The idea is a semiclassical analog of the Poincare model of the electron, where the outward classical electromagnetic stress is replaced by the stress due to vacuum polarization. Here the electron carries a bare mass (energy) due to negative pressure or equivalently a positive energy density inside and QED electromagnetic self-energy and both dependent on a cut-off radius R. Minimization of total energy with respect to R, yields a relation connecting equilibrium radius, negative pressure P, renormalized fine structure constant and lepton mass. Assumption that the maximum possible value of P corresponds most massive tau lepton is Planck pressure, enables determination of the renormalized fine structure constant and input of masses of the electron and muon determines corresponding internal negatives pressures and lepton radii. Tau lepton size is of the order of the Planck length and the muon and the electron are two and three orders of magnitude larger. Model suggests that the lepton flavor is an attribute associated with three different phases of a false vacuum.