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 (GEᵖ, GMᵖ, GEⁿ, GMⁿ, GER and GMR) systematically in a constituent quark model. Three ingredients are crucial in this study: i) the mixing of the |70, ²8,2,0,(1/2)^+ and the |56, ²8,0,0,(1/2)^+ which produces a nonzero neutron electric form factor. ii) a running coupling constant that soften the form factors. iii) the running quark mass function, Mq(p²), which is responsible for the decreasing of the μₚ GEᵖ(Q²)/GMᵖ(Q²) as Q² increases. The produced elastic form factors of the proton and neutron match the corresponding experiment values fairly well. Our study shows that μₚ GEᵖ(Q²)/GMᵖ(Q²) ≈ Mq(Q²/9)/Mq(0) upto Q² ≈ 4 GeV². We give predictions on the elactic form factors of the roper resonance, the charge and magnetic radius of the roper resonance compared with proton are rRE/rᵖE ≈ rRM/rᵖM ≈ 1.5.