Exchange Currents in Baryons

Abstract

This paper reviews calculations of the electromagnetic properties of baryons using the constituent quark model. We start with a short discussion of spontaneous chiral symmetry breaking, which is essential in understanding the transition from QCD to the constituent quark model. We then discuss a chiral version of the constituent quark model, which simulates the symmetries and dynamical content of the underlying field theory in terms of gluon, pion and sigma exchange between constituent quarks. We show that the electromagnetic current charge and current operators, usually approximated by one-body operators (impulse approximation), must be supplemented by appropriate two-body terms (exchange currents). The latter represent the gluon and pion exchange degrees of freedom in the electromagnetic current operator. These exchange currents must be included for reasons of completeness and consistency. Most importantly, however, they are needed in order for the electromagnetic current to be conserved. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. By including these twobody exchange currents we go beyond the single-quark impulse approximation, which has mainly been used up to now. The inclusion of gluon- pion-, and scalar-exchange currents in the quark potential model is the new point of the present work. We show that for some observables, such as the magnetic moments, charge, and magnetic radii of the proton and charged Δ (1232) states, exchange currents contribute at the level of some 10%. The same holds true for the magnetic moments of the entire baryon octet, with the exception of the Ξ- magnetic moment. On the other hand, the neutron charge radius, the quadrupole moments of the Δ, and the N → Δ transition quadrupole moment, are dominated by pion and gluon exchange contributions to the charge density operator. The inclusion of the pion and gluon exchange currents leads to a neutron charge radius of the correct size and sign. Based on the gluon and pion exchange current diagrams, we derive parameter-free relations between the neutron charge radius, the quadrupole moment of the Δ, and the N → Δ transition quadrupole moment. Neglecting configuration mixing, we find that the neutron charge radius and the N → Δ transition quadrupole moment are simply related as QN→Δ = r2 n√2. The implications of Siegert's theorem for the calculation of the E2 form factor in the N → Δ transition are studied. Finally, we discuss the axial coupling constant of the nucleon. We show that the inclusion of axial pair exchange currents does not significantly alter the NRQM prediction.