Nucleon to Delta electromagnetic transition in the Dyson-Schwinger approach

TL;DR

This paper models the N-Delta electromagnetic transition using the Dyson-Schwinger approach, finding good agreement with experimental data for certain form factors and highlighting the role of Poincare covariance and p-wave contributions.

Contribution

It introduces a self-consistent Dyson-Schwinger framework for N-Delta transitions treating baryons as quark-diquark bound states, excluding pion-cloud effects.

Findings

R_EM and R_SM form-factor ratios agree with experimental data

Magnetic dipole form factor underestimates data by ~25% at static limit

Static properties are insensitive to quark mass variations

Abstract

We study the N-Delta-gamma transition in the Dyson-Schwinger approach. The nucleon and Delta baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R_EM and R_SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves in the nucleon and Delta bound-state amplitudes which are a consequence of Poincare covariance. On the other hand, the dominant transition amplitude, i.e. the magnetic dipole transition form factor, underestimates the data by ~25% in the static limit whereas agreement is achieved at larger momentum transfer, which is consistent with missing pion-cloud contributions. We furthermore find that the static properties of the form factors are not very sensitive to a variation of the current-quark mass.