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

Andrea Mejia and Peter Schweitzer

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Phys. Rev. D 113, 054016 – Published 11 March, 2026

DOI: https://doi.org/10.1103/yf8j-6dwm

Abstract

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  GeV2 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  GeV2, 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.

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Phys. Rev. D 113, 054016– Published 11 March, 2026
  • Received 23 December 2025
  • Accepted 11 February 2026
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