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?


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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