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As we known, we introduce Higgs mechanism into Standard model to explain mass of Gauge boson, lepton and neutrino(maybe?). Higgs mechanism is necessary for electroweak theory because gauge symmetry and chiral symmetry.

But in QCD, Is Higgs mechanism still necessary? It seems there is no chiral symmetry in QCD so that mass of quark not necessarily to be zero. And on the other hand, gluon seems to be massless(maybe I am wrong?mass of proton). It seems like Higgs mechanism is not a necessary in QCD.

Is my understanding right? Thanks a lot!

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quarks are doublets - a mass is still forbidden by su2. You may have heard that hadron mass is mainly from as strong dynamics, which is correct. –  innisfree Oct 18 '13 at 16:46
    
@HuaWei Yes, gluons are massless. –  user29727 Oct 18 '13 at 16:47
    
@innisfree But is SU(2) necessary in QCD? Just like QED, we can have massive dirac field without Higgs mechanism. –  Hua Wei Oct 18 '13 at 16:52
    
Quarks interact with eg W boson. its necessary that quarks are in left-handed su2 doublets, which prohibits an explicit mass prior to symmetry breaking –  innisfree Oct 18 '13 at 16:55
    
(Left-Handed) Quarks obeys weak interaction too, and $Z_0, W^{\pm}$ are the gauge bosons of the weak interaction. –  Trimok Oct 18 '13 at 17:00
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up vote 5 down vote accepted

That really depends on what you call necessary.

If you completely forget all about $SU(2)_L$ (say, in an alternate universe with no Weak Interactions). Then mass terms in the Lagrangian for quarks and leptons are not forbidden by any symmetry and you would not need the Higgs field to generate the mass of the quarks or of the electron.

Now, in OUR universe, all those particles interact weakly and then mass terms are forbidden and you need the Higgs to give masses to quarks and leptons.

The mass of the proton, on the other side, has very little to do with the Higgs. Consider that the light quarks that compose the proton have a pole mass of a few MeV (2 to 4 MeV), while the proton itself masses ~900 MeV. Where does the extra mass comes from?

The answer is binding energy. The quarks interact very strongly and the mass of the proton is the combination of the three real quarks plus a whole lot of virtual quarks and gluons. Even if we had no Higgs and the masses of all those guys were zero, the proton mass would not change much.

Since most of the visible mass in the universe is made of protons and neutrons, it is a bit of a fallacy to say that the Higgs field "is responsible for all mass". It is certainly responsible for the mass of elementary particles, but QCD is what generates "our mass". If anyone wants to check what would change if we did not have the Higgs, there is a good paper by Chris Quigg (http://arxiv.org/pdf/0901.3958v2.pdf), which also has a deeper discussion on mass generation by QCD.

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Thanks a lot! That is really helpful –  Hua Wei Oct 18 '13 at 20:27
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