Energy-momentum tensor form factor D ( t ) of the proton and neutron

The energy-momentum tensor form factor D ( t ) is finite and negative in hadronic models and lattice QCD when only strong forces are included. However, when electromagnetic forces are considered, the D ( t ) of charged hadrons undergoes a dramatic change: at small t , it changes sign and diverges like 1 / − t as shown for the proton in the classical model by Białynicki-Birula based on residual nuclear forces which can be understood as a mean field approach. We construct an analogous neutron model and show that this framework accurately explains the electromagnetic proton-neutron mass difference. We demonstrate that, after appropriately rescaling the residual nuclear forces, the model can reproduce lattice data on the nucleon D ( t ) up to ( − t ) ≲ 1 GeV 2 as well as QED effects. Based on this realistic model description, we show that the proton and neutron D ( t ) form factors are practically indistinguishable down to ( − t ) ≈ 10 − 4 GeV 2 , far below what can currently be accessed experimentally. We conclude that in the foreseeable future the D ( t ) form factors of the proton and neutron will practically look the same in experiments and phenomenology.