On the physics behind the form factor ratio ${\mu }_p{G}_E^p(Q^2)\mathrm{/}{G}_M^p(Q^2)$

We point out that there exist two natural definitions of the nucleon magnetization densities : the density ${\rho }_M^K(r)$ introduced in Kelly’s phenomenological analysis and theoretically more standard one ${\rho }_M(r)$. We can derive an explicit analytical relation between them, although Kelly’s density is more useful to disentangle the physical origin of the different $Q^2$ dependence of the Sachs electric and magnetic form factors of the nucleon. We evaluate both of ${\rho }_M(r)$ and ${\rho }_M^K(r)$ as well as the charge density ${\rho }_{ch}(r)$ of the proton within the framework of the chiral quark soliton model, to find a noticeable qualitative difference between ${\rho }_{ch}(r)$ and ${\rho }_M^K(r)$, which is just consistent with Kelly’s result obtained from the empirical information on the Sachs electric and magnetic form factors of the proton.