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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?

Il Guercio
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    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. – Cosmas Zachos Sep 28 '23 at 14:07
  • @CosmasZachos Aren't the current quarks the constituent quarks then? – Il Guercio Sep 28 '23 at 14:36
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    Ab Initio Determination of Light Hadron Masses, Science 21 Nov 2008, Vol 322, Issue 5905, pp. 1224-1227, DOI: 10.1126/science.1163233 – John Rennie Sep 28 '23 at 14:44
  • Constituent quarks are already renormalized, so there's nothing to calculate by definition. Your question should probably something like: "Has the mass of a proton been calculated from current quarks, through the renormalization process?" – Miyase Sep 28 '23 at 14:44
  • @Miyase Thanks. I'll edit. – Il Guercio Sep 28 '23 at 14:46
  • related: https://physics.stackexchange.com/q/474084/50583 – ACuriousMind Sep 28 '23 at 14:49
  • As for answering the question, I left this field years ago and now only follows it superficially, but as far as I know the full renormalization process from current quarks to valence quarks has never been explicitely done. @JohnRennie 's link above might prove me wrong, but it's behind a paywall so I can't check the details. – Miyase Sep 28 '23 at 14:51
  • 0f course not the light quarks in the QCD Lagrangian are a few MeVs, but the constituent ones are about 350MeV. They've been basically abandoned by 1980... – Cosmas Zachos Sep 28 '23 at 15:00
  • @CosmasZachos But is the mass of constituent quarks, which obviously is about 350 MeV (as the mass of the proton is about 938 MeV), but what gives the naked quarks a higher mass? Their speed? Does that compensate for the binding energy? – Il Guercio Sep 28 '23 at 15:14
  • Residual nonperturbative QCD interactions in a chiral symmetry breaking domain... You really can't cook up a simple model, even though FKR tried, in the early 70s, before the triumph of QCD. But why are you barking up this wrong tree? – Cosmas Zachos Sep 28 '23 at 15:18
  • a review of lattice qcd for mass calculations , open, https://arxiv.org/pdf/0906.0126.pdf – anna v Sep 28 '23 at 17:21
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    I'll edit. The body still talks about “interactions between the constituent quarks”, so now the title and body are in conflict. – Ghoster Sep 28 '23 at 17:25
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    @IlGuercio hadrons are much more complicated than their named constituent quarks . have a look https://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/whats-a-proton-anyway/ – anna v Sep 28 '23 at 17:29
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    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," https://arxiv.org/pdf/1111.5960.pdf – anna v Sep 28 '23 at 17:44
  • @Ghoster Ah, yes! Thanks. I'll edit it again... – Il Guercio Sep 28 '23 at 18:01
  • @CosmasZachos Is it possible then to calculate the masses of the dressed-up quarks, including all virtual happenings? And how big is the part of the momentum increase of the quarks? Does that contribute to the effective mass increase? I think that basically, I'm asking how to calculate both the 350 MeV of the constituent quarks, and the -112 MeV binding energy. – Il Guercio Sep 28 '23 at 19:38
  • You are asking how to match the chiral bag σ model through lattice QCD simulations, which is terribly hard, and I have never heard of a realistic attempt-- even though, decades ago, there were rumors Wilson & LePage were thinking about it. Possible, in principle, but impossibly hard in practice... – Cosmas Zachos Sep 28 '23 at 21:21
  • "Ab-initio Determination of Light Hadron Masses" https://arxiv.org/abs/0906.3599 – alanf Sep 29 '23 at 06:54

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