Note on the magnetic moment of the nucleon

Abstract

The Goldberger-Treiman relation $M=2\pi /\sqrt{3}{f}_{\pi }^{\mathrm{cl}}$ where $M$ is the constituent quark mass in the chiral limit (cl) and $f_{\pi }^{\mathrm{cl}}$ the pion decay constant in the chiral limit predicts constituent quark masses of $m_u=328.8\pm 1.1$ MeV and $m_d=332.3\pm 1.1$ MeV for the up and down quark, respectively, when $f_{\pi }^{\mathrm{cl}}=89.8\pm 0.3$ MeV is adopted. Treating the constituent quarks as bare Dirac particles the following zero order values \mu^{(0)}}_p=2.850\pm 0.009 and \mu^{(0)}}_n= -1.889\pm 0.006 are obtained for the proton and neutron magnetic moments, leading to deviations from the experimental data of 2.0% and 1.3%, respectively. These unavoidable deviations are discussed in terms of contributions to the magnetic moments proposed in previous work.