Light-front representation of chiral dynamics with Δ isobar and large-N c relations

Abstract

Transverse densities describe the spatial distribution of electromagnetic current in the nucleon at fixed light-front time. At peripheral distances b = O(M_pi^{-1}) the densities are governed by chiral dynamics and can be calculated model-independently using chiral effective field theory (EFT). Recent work has shown that the EFT results can be represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft-pion-nucleon intermediate states, resulting in a quantum-mechanical picture of the peripheral transverse densities. We now extend this representation to include intermediate states with Delta isobars and implement relations based on the large-N_c limit of QCD. We derive the wave function overlap formulas for the Delta contributions to the peripheral transverse densities by way of a three-dimensional reduction of relativistic chiral EFT expressions. Our procedure effectively maintains rotational invariance and avoids the ambiguities with higher-spin particles in the light-front time-ordered approach. We study the interplay of pi-N and pi-Delta intermediate states in the quantum-mechanical picture of the densities in a transversely polarized nucleon. We show that the correct N_c-scaling of the charge and magnetization densities emerges as the result of the particular combination of currents generated by intermediate states with degenerate N and Delta. The off-shell behavior of the chiral EFT is summarized in contact terms and can be studied easily. The methods developed here can be applied to other peripheral densities and to moments of the nucleon's generalized parton distributions.