Nucleon form factors in an independent-quark model based on Dirac equation with power-law potential.

Abstract

The nucleon electromagnetic form factors ${G}_{E}^{p}$(${q}^{2}$) and ${G}_{M}^{p}$(${q}^{2}$) and the axial-vector form factor ${G}_{A}$(${q}^{2}$) are investigated in a simple model of relativistic quarks confined by a vector-scalar mixed potential ${U}_{q}$(r)=(1+${\ensuremath{\gamma}}^{0}$)(${a}^{\ensuremath{\nu}+1}$${r}^{\ensuremath{\nu}}$ +${V}_{0}$) without taking into account the center-of-mass correction and the pion-cloud effects. The respective rms radii associated with ${G}_{E}^{p}$(${q}^{2}$) and ${G}_{A}$(${q}^{2}$) come out as 〈${r}_{c}$${\mathrm{}}^{2}$${〉}^{1/2}$=1.07 fm and 〈${r}_{A}$${\mathrm{}}^{2}$${〉}^{1/2}$=1.17 fm. The possibility of restoring in this model the chiral symmetry in the usual way is discussed and the pion-nucleon form factor ${G}_{\ensuremath{\pi}\mathrm{NN}}$(${q}^{2}$) is derived. The pion-nucleon coupling constant is obtained as ${g}_{\ensuremath{\pi}\mathrm{NN}}$=10.2, as compared to (${g}_{\ensuremath{\pi}\mathrm{NN}}$${)}_{\mathrm{expt}\mathrm{\ensuremath{\simeq}}}$13.