Reconstructed baryon transition current structure of the N(1520) longitudinal amplitude: Insights from Patterson function analysis

Abstract

The spatial structure of baryon transition currents provides valuable insight into nucleon excitations beyond what can be inferred from transition form factors alone. In this work, the Patterson function is applied to reconstruct the transition current density associated with the N(1520) longitudinal amplitude. The resulting distribution exhibits a highly localized positive core with a half-maximum radius of 0.0745 fm, surrounded by an extended negative shell. The reconstructed density reaches a central maximum of approximately 1700 fm⁻³ and a minimum of −266 fm⁻³ at r = 0.171 fm, indicating a pronounced oscillatory structure within a compact spatial region. Comparison with previously reconstructed baryon transition currents shows that the N(1520) longitudinal amplitude possesses one of the deepest negative minima among the resonances examined, distinguishing its internal organization from those of the Δ(1232), N(1440), and N(1535) excitations. The close agreement between independent reconstructions further supports the robustness of the Patterson methodology. These results demonstrate that Patterson function analysis provides a model-independent framework for obtaining spatially explicit images of transition current distributions and complements theoretical approaches based on parametrized form factors and lattice QCD calculations.