Light Quark Hadron Mass Scale

Abstract

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(Dμ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m0/M = g2. This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group Gspin × GD gives the light quark hadron degenerate multiplet mass spectrum in terms of m0[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em0/nM for light quarks is the quark charge e/3 renormalized by m0/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m0−1. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .