It is a well-established fact that the main contribution to the mass of proton is the gluonic field inside a proton, as some answers explain (see here and here). But being the proton and the neutron remarkably similar in structure, I wonder how much the electromagnetic field contributes to the mass difference. And if it is not due to the electromagnetic field, what would be the cause for the mass difference between the proton and the neutron.
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1$\begingroup$ As the linked pages indicate, it's complicated! EM energy is fairly minor compared to the strong force, and because gluons exchange gluons you can't use the same Feynmann diagram tricks that work for QED. Frank Wilczek's early rough QCD calculation of proton mass from first principles consumed months of computer time on a Cray. We now have faster techniques & hardware, but they still don't give much precision to hadron mass calculations. $\endgroup$– PM 2RingCommented Aug 6, 2022 at 0:27
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The electromagnetic contribution to the proton-neutron mass difference is a tiny effect of $0.58 \pm 0.16$ MeV. The main contribution to $m_p-m_n$ is a QCD effect (due to the mass difference of up and down quark): $-1.87 \pm 0.16$ MeV. See J. Gasser, H. Leutwyler, A. Rusetsky, arXiv 2003.13612 for details.
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2$\begingroup$ Because of color confinement, the mass of a quark is a bit of a nebulous concept, as Roger Barlow mentions in a comment to one of the linked questions. So it's tricky to disentangle the effects of quark mass from the effects of potential & kinetic energy. $\endgroup$– PM 2RingCommented Aug 6, 2022 at 20:10