That's basically my question. Has the mass of the proton been calculated using QCD and the interactions between the current quarks? Perturbative methods obviously can't be used as they deal with asymptotically free particles, and QFT isn't suited for that. If so, what methods were used, or could be used?

The naked quarks are considerably lighter than the dressed-up ones. The constituent quarks have a mass of about 350 MeV, which is more than one-third of the mass of the proton, which is 938 MeV. These quarks have a binding energy, which must be then 936-1050=-112 MeV. The naked quarks have a mass of about 1/100 of the dressed-up ones.

Is there a scheme to tackle this problem? It's a pity I can't access the linked article in the comment section below. There is a paywall behind which the solution is allegedly given.

What is, for example, the biggest contribution to the increase in mass of the three naked quarks? Has this effective mass increase been calculated? Is there a way to calculate the momentum of the current quarks in protons? Do they move at relativistic speed, effectively increasing their mass?

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    $\begingroup$ Are you sure you wish to talk about constituent quarks? Their effective theory is not quite QCD. I suspect you are talking about the current quarks in the QCD Lagrangian, a hundred times lighter. $\endgroup$ Commented Sep 28, 2023 at 14:07
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    $\begingroup$ Ab Initio Determination of Light Hadron Masses, Science 21 Nov 2008, Vol 322, Issue 5905, pp. 1224-1227, DOI: 10.1126/science.1163233 $\endgroup$ Commented Sep 28, 2023 at 14:44
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    $\begingroup$ I'll edit. The body still talks about “interactions between the constituent quarks”, so now the title and body are in conflict. $\endgroup$
    – Ghoster
    Commented Sep 28, 2023 at 17:25
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    $\begingroup$ @IlGuercio hadrons are much more complicated than their named constituent quarks . have a look profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/… $\endgroup$
    – anna v
    Commented Sep 28, 2023 at 17:29
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    $\begingroup$ and here is a lecture on the subject presented in 2018 at "the Erice School on Nuclear Physics: From Quarks and Gluons to Hadrons and Nuclei," arxiv.org/pdf/1111.5960.pdf $\endgroup$
    – anna v
    Commented Sep 28, 2023 at 17:44


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