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

The energy-momentum tensor (EMT) 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 $1/\sqrt{-t}$ as shown for the proton in the classical model by Bia{\l}ynicki-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 $(-t)\lesssim 1\,$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 $(-t) \approx 10^{-4}\rm GeV^2$ far below what can currently be accessed experimentally. We conclude that in the foreseeable future the $D(t)$ form factors of proton and neutron will practically look the same in experiments and phenomenology.