Running Coupling and Running Quark Mass Effects on the Elastic Form Factors of Nucleons
We study the elastic electric and magnetic form factors of the proton, neutron and the charged roper resonance ($G_E^p$, $G_M^p$, $G_E^n$, $G_M^n$, $G_E^R$ and $G_M^R$) systematically in a constituent quark model. Three ingredients are crucial in this study: i) the mixing between the pure S-wave and other components which produces a nonzero neutron electric form factor. ii) a running coupling constant that soften the form factors. iii) the running quark mass function, $M_q(p^2)$, which is responsible for the decreasing of the $μ_p G_E^p(Q^2)/G_M^p(Q^2)$ as $Q^2$ increases. The produced elastic form factors of the proton and neutron match the corresponding observed values fairly well. Our study shows that $μ_p G_E^p(Q^2)/G_M^p(Q^2) \approx M_q(Q^2/9)/M_q(0)$ upto $Q^2 \approx 4 \text{ GeV}^2$. We give predictions on the elastic form factors of the roper resonance, the electric charge and the magnetic momentum radius ratios of the roper resonance to the proton are $r^R_{E}/r^p_{E} \approx r^R_{M}/r^p_{M} \approx 1.5$.