Can massless quarks form massive hadrons?

In summary, the mass of hadrons is mostly generated by the mechanism of spontaneous chiral symmetry breaking in QCD, rather than the mass of the quarks themselves. This also has implications for the electroweak interaction, as QCD's symmetry breaking could potentially contribute to the masses of the W and Z bosons. However, the observed masses of these bosons are much larger than expected, leading to alternative theories such as technicolor.
  • #1
carroza
7
0
It is clear that the mass of the valence quarks is only a small fraction of the mass of the hadrons (for example, the proton).

However, I wonder if it would be possible to get massive protons in QCD if the quarks were truly massless.

On one hand, for massless quarks, the pions, as Goldstone bosons of an exact Chiral symmetry, would be massless.

On the other hand, the binding energy of any electron-positron bound state would vanish in the limit of zero electron(positron) mass.

Is there some general argument to exclude in QCD finite masses for systems of masless quarks?
In the case of glueballs (made of massless gluons), do they have finite mass?
 
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  • #2
QCD is a funny theory - it exibits asymptotic freedom, and (presumably) there is a mechanism of "chiral symmetry breaking" that gives a vev to the quark bilinear of order a few hundred MeV. It is THIS scale that generates masses for the hadrons! This leads to a very amusing statement: if there were no Higgs at all, the W/Z bosons would be 1 GeV, NOT massless (this is a famous qualifying exam question for particle physicists looking to get a PhD!).

Of course, now you ask - where does this chiral symmetry breaking come from? Answer that, and you are on your way to winning $1,000,000 from the Clay Math Institute!

So in answer to your question: the mass of the hadrons presumably comes from the (as yet not well understood) QCD dynamics that generate a mass gap - quark mass is a relatively small contribution compared to this. So yes: glueballs are massive. Proof of this will win you lots of $$ ;-)

Hope this helps!
 
  • #3
blechman said:
QCD is a funny theory - it exibits asymptotic freedom, and (presumably) there is a mechanism of "chiral symmetry breaking" that gives a vev to the quark bilinear of order a few hundred MeV. It is THIS scale that generates masses for the hadrons! This leads to a very amusing statement: if there were no Higgs at all, the W/Z bosons would be 1 GeV, NOT massless (this is a famous qualifying exam question for particle physicists looking to get a PhD!).

Thank you for your answer. There are a couple of things from it that i do not understand yet:

What is a "vev" ?

Why the W/Z bosons, which are associated to weak and electromagnetic interactions, should remain massive if there was no Higgs? What is the link between QCD and W/Z bosons?
 
  • #4
carroza said:
What is a "vev" ?

vev = "Vacuum Expectation Value" - this is the thing that breaks the symmetry. Take a look at any book or website that describes "Spontaneous Symmetry Breaking" for more details.

Why the W/Z bosons, which are associated to weak and electromagnetic interactions, should remain massive if there was no Higgs? What is the link between QCD and W/Z bosons?

This is subtle, and perhaps I should not have mentioned it if it confuses you. The thing is - the spontaneous chiral symmetry breaking that happens in QCD also breaks the electroweak symmetry (since EW theory is a chiral gauge theory) - it wasn't planned, it was just an accident, but there you are. Therefore it would contribute to the W and Z masses. If they were 1 GeV each, we would have a complete theory of electrweak physics! However, they are 2 orders of magnitude heavier than that, so this cannot be the only source of the symmetry breaking. These ideas are the basis of an alternative theory called "technicolor" which is just like QCD with the scale cranked up to a TeV. Unfortunately, this theory does not describe the precision measurements that we have been making since the 1980's, so it probably isn't correct (at least in its naive form).

So the short answer is: QCD has nothing to do with W/Z masses in the world that we live in. But it could have.
 
  • #5
vev is the vacuum expectation value as mentioned before,but breaks the symmetry only when taking non zero value
 

1. What is a massless quark?

A massless quark is a type of elementary particle that has no mass. Quarks are the building blocks of protons and neutrons, which make up the nuclei of atoms. There are six types of quarks, and each one has a different mass except for the top and bottom quarks, which are considered to be nearly massless.

2. Can massless quarks form massive hadrons?

No, massless quarks cannot form massive hadrons. In order for a hadron (such as a proton or neutron) to have mass, its constituent quarks must also have mass. Massless quarks would result in a hadron with no mass, which is not observed in nature.

3. How do we know that quarks have mass?

Scientists have observed the effects of quark mass through experiments and calculations. For example, the behavior of quarks in particle accelerators and the properties of hadrons (such as their mass and spin) provide evidence for the existence of quark mass.

4. Can quarks change from being massless to having mass?

No, quarks cannot change from being massless to having mass. Quarks are considered to be fundamental particles, meaning they cannot be broken down into smaller components. Therefore, their mass is an inherent property and cannot be changed.

5. Why is it important to understand the relationship between massless quarks and massive hadrons?

Understanding the relationship between massless quarks and massive hadrons is important because it provides insight into the fundamental forces and particles that make up our universe. It also helps us better understand the behavior of matter and the properties of different types of particles. Additionally, this knowledge can have practical applications in fields such as particle physics and cosmology.

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