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

In summary, the conversation discusses the concept of "massless quarks" in QCD and how it relates to the equation E = \pm \sqrt{p^2 + m^2}. It is clarified that while quarks are not truly massless, their masses can be approximated as zero in certain scenarios. The conversation also mentions constituent quarks and current quarks, and how their masses differ. Finally, the Nambu-Jona-Lasinio model is briefly mentioned as a way to explain the masses of quarks.
  • #1
StatMechGuy
223
2
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
[tex]
E = \pm \sqrt{p^2 + m^2}
[/tex]
the [tex]p^2[/tex] term dominates and [tex]E \sim p[/tex] or is this something completely different?
 
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  • #2
Massless particles have p > 0 but m = 0, so E = p (assuming you have set c = 1).
 
  • #3
Yes, but quarks are decidedly not massless in the m=0 sense.
 
  • #4
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.
 
  • #5
milou said:
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.
 
  • #6
kcrick said:
milou said:
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? :)
 
Last edited by a moderator:

1. What are massless quarks?

Massless quarks are elementary particles that have no rest mass. They are a fundamental component of matter and are believed to be the building blocks of protons and neutrons.

2. How do massless quarks differ from massive quarks?

The main difference between massless and massive quarks is their mass. Massless quarks have no measurable mass, while massive quarks have a finite mass. This affects their behavior and interactions with other particles.

3. Can massless quarks exist in isolation?

No, massless quarks cannot exist in isolation. They are always found in composite particles, such as protons and neutrons. This is due to a phenomenon known as confinement, where quarks are bound together by the strong nuclear force.

4. How do massless quarks contribute to the Standard Model of particle physics?

Massless quarks are an essential part of the Standard Model, which is a theory that describes the fundamental particles and their interactions. They are one of the six types of quarks, and their properties and behavior are crucial in understanding the behavior of matter at the smallest scales.

5. Are there any implications of the existence of massless quarks?

Yes, the existence of massless quarks has significant implications in the study of particle physics and the behavior of matter. It has also led to the development of various theories and models, such as quantum chromodynamics, to explain the properties and interactions of these particles.

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