SU(6) breaking effects in the nucleon elastic electromagnetic form factors

Abstract

The effects of both kinematical and dynamical SU(6) breaking on the nucleon elastic form factors, $G_E^N{(Q}^2)$ and $G_M^N{(Q}^2),$ are investigated within the constituent quark model formulated on the light front. The investigation is focused on $G_E^n{(Q}^2)$ and the ratio $G_M^p{(Q}^2{)/G}_M^n{(Q}^2),$ which within the SU(6) symmetry are given by $G_E^n{(Q}^2)=0\mathrm{}$ and $G_M^p{(Q}^2{)/G}_M^n{(Q}^2)=-3/2,$ respectively. It is shown that the kinematical SU(6) breaking caused by the Melosh rotations of the quark spins as well as the dynamical SU(6) breaking due to the mixed-symmetry component generated in the nucleon wave function by the spin-dependent terms of the quark-quark interaction, can affect both $G_E^n{(Q}^2)$ and $G_M^p{(Q}^2{)/G}_M^n{(Q}^2).\mathrm{}$ The calculated $G_E^n{(Q}^2)$ is found to be qualitatively consistent with existing data, though only $\simeq 65\%$ of the experimental neutron charge radius can be explained without invoking effects from possible nonvanishing sizes of the constituent quarks and/or many-body currents. At the same time the predictions for the magnetic ratio $G_M^p{(Q}^2{)/G}_M^n{(Q}^2)$ turn out to be inconsistent with the data. It is, however, shown that the calculations of $G_M^N{(Q}^2)$ based on different components of the one-body electromagnetic current lead to quite different results. In particular, the calculations based on the plus component are found to be plagued by spurious effects related to the loss of the rotational covariance in the light-front formalism. These unwanted effects can be avoided by considering the transverse y component of the current. In this way our light-front predictions are found to be consistent with the data on both $G_E^n{(Q}^2)$ and $G_M^p{(Q}^2{)/G}_M^n{(Q}^2).\mathrm{}$ Finally, it is shown that a suppression of the ratio $G_E^p{(Q}^2{)/G}_M^p{(Q}^2)$ with respect to the dipole-fit prediction can be expected in the constituent quark model provided the relativistic effects generated by the Melosh rotations of the constituent spins are taken into account.