standard model - Is a quark‘s constituent mass affected by the chiral limit?

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?

Answer

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.