# Is Higgs mechanism necessary in QCD?

As we know, the Higgs mechanism is introduced in the Standard model in order to explain the masses of the gauge bosons, the leptons and the neutrinos (maybe?). The Higgs mechanism is necessary to introduce masses in electroweak theory because of gauge symmetry and chiral symmetry.

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

Is my understanding right? Thanks a lot!

• 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. 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. 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 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. Oct 18 '13 at 17:00

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.