Electromagnetic form factors of the nucleon from the instanton vacuum

Abstract

We investigate the electromagnetic form factors of the nucleon within an effective chiral theory derived from the QCD instanton vacuum, taking into account the finite current quark mass. The momentum-dependent dynamical quark mass, generated by the instanton-antiinstanton medium, naturally plays the role of a regulator, so that no additional regularization is required to tame the divergences arising from quark loops. The instanton parameters, the average instanton size $\bar{\rho}=0.35$ fm and the average interdistance $\bar{R}=0.86$ fm, together with the dynamical quark mass at zero virtuality $M_0=385$ MeV, are all fixed by the saddle-point equation beyond the chiral limit, leaving no adjustable free parameter in the present calculation. We compute the Sachs electric and magnetic form factors of the proton and neutron, the nucleon charge and magnetization radii, the magnetic moments, and the ratios $\mu_{p,n} G_E^{p,n}(Q^2)/G_M^{p,n}(Q^2)$. The present results are compared with the experimental data, the chiral quark-soliton model ($\chi$QSM), and the Kelly parametrization. The proton charge radius, $\sqrt{\langle r^2 \rangle_\mathrm{ch}^p}=0.841$ fm, is in remarkable agreement with the recent muonic-hydrogen value, and the $Q^2$ dependence of the proton form-factor ratio $\mu_p G_E^p/G_M^p$ is reproduced very well, in clear contrast to the $\chi$QSM. The overall agreement with the experimental data confirms that the effective chiral theory derived from the QCD instanton vacuum provides a consistent and predictive framework for describing the electromagnetic structure of the nucleon.