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The up- and down quark’s constituent mass is usually taken to be around $300\,\text{MeV}\approx \tfrac{1}{3} m_\text{proton}$. Is this quantity affected by the chiral limit, where we let the quarks’ running mass go to zero?

If so, how?

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Well, yes and no, but essentially no.

The constituent masses for the d and u, respectively, are 336 and 340MeV.

Their respective current masses are 4.3-5.2MeV and 1.8-2.8MeV.

So the current masses are negligible w.r.t. the constituent ones, of the order of 1%. Moreover, as you see, the current u is lighter than the d, but after chiral symmetry breaking the u is ever so slightly heavier than the d. There is a lot of slop in these determinations, and also electromagnetic effects, etc.

The takeaway expectation, then, is that setting the current masses equal to 0 would not take you far away from 330MeV.

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  • $\begingroup$ Does this mean that a quark‘s current mass and the dynamically generated mass are completely unrelated? $\endgroup$ – Stephan Oct 2 '18 at 2:31
  • $\begingroup$ They are weakly related, in a non-obvious way. $\endgroup$ – Cosmas Zachos Oct 2 '18 at 2:46
  • $\begingroup$ I see. Do you know where I could do some further reading? I tried searching on the arXiv, but apparently I haven’t found the right papers yet. $\endgroup$ – Stephan Oct 2 '18 at 3:32
  • $\begingroup$ Perhaps the lattice gauge articles pinning down the current masses...... $\endgroup$ – Cosmas Zachos Oct 2 '18 at 10:15
  • $\begingroup$ Are you referring to quark condensation by ud mass after chiral symmetry breaking? $\endgroup$ – Turgon Oct 6 '18 at 5:37

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