Classical Models of the Neutron and Proton: Insights on the Energy-Momentum Tensor and the D-term

The description of the structure of the nucleon requires a relativistic quantum field theoretical framework. However, studies in classical relativistic field theories can offer clearer insights into fundamental properties without the intricate quantum corrections. This is particularly valuable when examining aspects tied to the long-range nature of electromagnetic interactions. Using the classical proton model developed by Bialynicki-Birula has especially revealed the profound influence of the long-range Coulomb force on the D-term form factor, which has been previously overlooked in models and lattice studies of quantum chromodynamics (QCD). This investigation involves transforming Bialynicki-Birula's classical "dust particle" field model into an adequate​ classical model​ of the neutron. We compute the neutron​ D-term and draw a comparison with the proton's D-term, which was noted to exhibit a divergence due to the influence of the classical Coulomb field. Notably, our findings confirm​ that the regularization approach​ proposed​ for the proton D-term is reasonable because it gives numerically very similar results to the neutron D-term.