Light-Front Transverse Nucleon Charge and Magnetisation Densities

Nucleon elastic electromagnetic form factors obtained using both the three-body and quark + fully-interacting-diquark pictures of nucleon structure are employed to calculate an array of light-front transverse densities for the proton and neutron and their dressed valence-quark constituents, viz. flavour separations of the proton and neutron results. These two complementary descriptions of nucleon structure deliver mutually compatible predictions, which match expectations based on modern parametrisations of available data, where such are available. Amongst other things, it is found that transverse-plane valence $u$- and $d$-quark Dirac radii are practically indistinguishable; but regarding kindred Pauli radii, the $d$ quark value is roughly 10% greater than that of the $u$-quark. Moreover, magnetically, the valence $d$ quark is far more active than the valence $u$ quark, probably because it has much greater orbital angular momentum. Both pictures of nucleon structure agree in predicting that, in a polarised nucleon, the transverse-plane charge densities are no longer rotationally invariant. Instead, for a $+\hat x$ polarised nucleon, positive charge is displaced in the $+\hat y$ direction, with the opposite effect for negative charge.

💡 Research Summary

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This paper presents a comprehensive study of the transverse charge and magnetisation densities of the proton and neutron using two complementary continuum‑Schwinger‑method (CSM) approaches to nucleon structure. The first approach solves the three‑body Faddeev equation for the nucleon’s bound‑state amplitude, while the second treats the nucleon as a quark plus a fully interacting diquark (q‑qq) correlation. Both frameworks are Poincaré‑covariant and employ the rainbow‑ladder (RL) truncation of the Dyson‑Schwinger equations (DSEs), ensuring a systematic connection to the underlying QCD Lagrangian.

The interaction kernel ˜G(y) used in the RL truncation combines an infrared‑dominant Gaussian term with a logarithmic ultraviolet tail, reproducing confinement (via violation of reflection positivity) and asymptotic freedom. With ω = 0.8 GeV and D = 0.8 GeV³ the kernel yields realistic hadron observables (pion mass, nucleon mass, pion decay constant) without further parameter tuning. The dressed quark propagator S(k)=Z(k²)/