Wavefunction-independent relations between the nucleon axial-coupling gA and the nucleon magnetic moments

Abstract

We calculate the proton's magnetic moment μ p and its axial-vector coupling g A as a function of its Dirac radius R 1 using a relativistic three-quark model formulated on the light-cone. The relationship between μ p and g A is found to be independent of the assumed form of the light-cone wavefunction. At the physical radius R 1 = 0.76 fm, one obtains the experimental values for both μ p and g A , and the helicity carried by the valence u and d quarks are each reduced by a factor ∽ 0.75 relative to their non-relativistic values. At large proton radius, μ p and g A are given by the usual non-relativistic formulae. At small radius, μ p becomes equal to the Dirac moment, as demanded by the Drell-Hearn-Gerasimov sum rule. In addition, as R 1 → 0, the constituent quark helicites become completely disoriented and g A → 0.