Understanding Massless Quarks in QCD and the Nambu-Jona-Lasinio Model

[StatMechGuy]

I've been doing some reading on QCD, and I keep running into the notion of "massless quarks". Are they massless in the sense that if you look at
$$E = \pm \sqrt{p^2 + m^2}$$
the $$p^2$$ term dominates and $$E \sim p$$ or is this something completely different?

 

[selfAdjoint]

Massless particles have p > 0 but m = 0, so E = p (assuming you have set c = 1).

 

[StatMechGuy]

Yes, but quarks are decidedly not massless in the m=0 sense.

 

[milou]

If you are talking about constitutent quarks, where three of them make up a baryon in the non-relativistic potential models, this is true. Then, mass is typically around 300 MeV.

However, if you are talking about current quarks - which are the relevant ones if you discuss partonic scattering, for example, the masses are 5 to 10 MeV for up and down quarks, and then, neglecting this mass may be quite a good approximation.

The idea is, for example, that you start with masseless current quarks which gain contituent quark masses by the spontaneous braeking of chiral symmetry, as, for example, in the Namb-Jona-Lasinio model.

 

[kcirick]

as, for example, in the Namb-Jona-Lasinio model.

My god... what happened to simple names for models these days? I can't even pronounce that model.

 

[selfAdjoint]

as, for example, in the Namb-Jona-Lasinio model.

My god... what happened to simple names for models these days? I can't even pronounce that model.

That should be http://en.wikipedia.org/wiki/Nambu-Jona-Lasinio_model" . "Namm-boo Joe-nah La-sin-eey-oh". How do you pronounce kcrick? :)