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

TL;DR

This paper models the electromagnetic effects on the energy-momentum tensor form factor D(t) of protons and neutrons, showing that their form factors are nearly identical at very low momentum transfer, with implications for experimental detection.

Contribution

The authors develop a residual nuclear force model incorporating electromagnetic effects to accurately describe the D(t) form factor of nucleons, matching lattice and QED data.

Findings

Electromagnetic forces cause D(t) of charged hadrons to change sign and diverge at small t.

The model reproduces lattice data for D(t) up to 1 GeV^2.

Proton and neutron D(t) form factors are nearly indistinguishable at very low momentum transfer.

Abstract

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.