Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D μ ) 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 m 0 /M = g 2 . 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 G spin × G D gives the light quark hadron degenerate multiplet mass spectrum in terms of m 0 [SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em 0 /nM for light quarks is the quark charge e /3 renormalized by m 0 /M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m 0 −1 . The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .