Wavefunction-Independent Relations between the Nucleon Axial-Coupling g_A and the Nucleon Magnetic Moments

Abstract

We calculate the proton's magnetic moment ${\mu }_p$ and its axial-vector coupling $g_A$ as a function of its Dirac radius $R_1$ using a relativisitic three-quark model formulated on the light-cone. The relationship between ${\mu }_p$ 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 ${\mu }_p$ and $g_A$, and the helicity carried by the valence $u$ and $d$ quarks are each reduced by a factor $\simeq 0.75$ relative to their non-relativistic values. At large proton radius, ${\mu }_p$ and $g_A$ are given by the usual non-relativistic formulae. At small radius, ${\mu }_p$ becomes equal to the Dirac moment, as demanded by the Drell-Hearn-Gerasimov sum rule. In addition, as $R_1\to 0,$ the constituent quark helicities become completely disoriented and $g_A\to 0$.

Comments: 17 pages, RevTeX, 4 uuencoded figures, SLAC-PUB-6431