The D-term form factor of the proton and neutron using a classical model and the comparison to Lattice QCD.

Fundamental properties of the proton and neutron, such as mass and spin, can be obtained from the matrix elements of the energy-momentum tensor (EMT) in terms of gravitational form factors (GFFs). An equally fundamental but less well-known property that can be extracted from the matrix elements of the EMT is the D-term form factor D(t), which describes the spatial distribution of forces inside a proton and neutron. Due to QED quantum loop effects, the D-term diverges in the proton while remains finite for the neutron. In our study, we use a classical relativistic model to calculate the D-term for the proton and neutron. Using realistic parameters informed by lattice QCD, we investigate whether or not our model can reproduce QCD and QED predictions, and whether this divergence can be seen below (-t) < -0.1GeV² in experiment ("t" being the momentum transfer squared between the electron and proton during a scattering event). Our model study shows this divergence of the proton’s D-term at (-t) < 10^-6 GeV², and supports that D(t) of the proton and neutron should look alike in experiments. We find that the model can not only reproduce the experimental value of proton charge radius and the proton-neutron electromagnetic mass difference, but also D(t) from lattice QCD calculations, being in agreement with lattice QCD predictions up to (-t) ~ 0.8 GeV². Based on a realistic description of the proton’s D(t) according to QCD and QED, we conclude that the divergence for small (-t) << 10^-6 GeV² in the proton will not be visible in experiments.