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The reason why the $u$-quark and the $d$-quark have different masses is that they couple with different Yukawa coupling strengths to the Higgs field. My understanding is that this is the sole reason for their mass difference. The fact that they have different charges does not source an additional mass difference.

However, this is not the case with the explanation of the mass difference between a neutron and a proton. The small mass difference between a neutron and a proton is said to arise PARTLY from electromagnetic interactions of the proton which the neutron does not feel.

Why does the electric charge difference cause a mass difference in the second case but not in the first case?

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  • $\begingroup$ Protons and neutrons are a whole lot more complicated than what is suggested here. $\endgroup$
    – my2cts
    Aug 10, 2021 at 21:22

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The electric potentials between the charges $+2e/3,\,+2e/3,\,-e/3$ in a proton contribute energy to the proton, with mass viz. $E=mc^2$. Unsurprisingly, the amount of such energy is a little different in the case of the neutron, where the charges are $+2e/3,\,-e/3,\,-e/3$.

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You are just reiterating the present picture of the SM, before any indications that pointlike quarks have any structure or size--even though there are some (poor) preon speculative models for such.

Recall $$ m_u\sim 2.16MeV, \qquad m_d\sim 4.67MeV, \qquad m_p\sim 938.27MeV, \qquad m_n\sim 939.57MeV, $$ while the size of the hadrons, about a fm, is huge on the scale of the respective Compton wavelengths!

That is, the quark masses are fundamental just-so inputs in the SM Lagrangian, while the hadron masses are "computable" (at least in lattice QCD) gap energies of furiously fluffy composite systems. Both QCD and QED treat the two hadrons differently, and actually decrease the respective isospin mass differences. The hapless work of the 50s & 60s on the baryon mass differences due to just electromagnetism is now all but deprecated, after the advent of lattice QCD. (For a modern theory estimate, consider this ref.)

  • So, the short answer to your question is that the quark mass difference is not computable in the present theoretical framework.

PS teachable moment. Gratuitous, irrelevant bonus point on isospin, often mistaught. You note the ratio of the masses of the two light quarks is about 1/2; so it is not true that their masses are almost equal that makes isospin a good approximate symmetry in the strong interactions. Instead, isospin is a good approximate symmetry because both (unequal) quark masses are small, almost negligible, w.r.t. the hadronization scale, $\Lambda_{QCD}$. This can be chased down experimentally.

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