# Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?

• in the page of your link, they point out the lack of confinement with chiral condensates in the theory
– user46925
Commented Jan 11, 2016 at 12:21

Well, in the NJL model you get rid of the gluon. They are considered to be frozen in the low energy limit where you are working because the mass is higher than the energy. Thus you are only working with quarks, and you consider interaction between quarks via effective coupling constants.

But in the standard model, gluons (seem to) acquire an effective mass because of confinement. That's why the range of the strong interaction is short. If you compare with photons, they have no electric charge and the range of the electromagnetic force is infinite.

• Gluons are massless. Short range of strong interaction is not due to them being massive.
– xi45
Commented May 4, 2016 at 13:23
• The bare mass of the gluon is zero. But due to the interaction it is considered to be dressed. See for example Origin of Mass from Frank Wilczek. Commented May 4, 2016 at 13:34
• Well, "gluons acquire a mass because they carry a color charge" is not correct. Then you can talk of glueballs, etc, if you wish.
– xi45
Commented May 4, 2016 at 13:40
• @xi45: it is more subtle than that. In the infrared, the gluon propagator saturates (i.e. does not diverge) as the momentum goes to zero, implying that the gluons are effectively massive, as it has been shown in lattice simulations.
Commented May 4, 2016 at 15:17
• @xi45: Well, at least it is measurable in "numerical experiments", i.e. lattice simulations (where we can get rid off the fermions). Unfortunately, I'm a dilettante, and I mostly follow the work of colleagues. But a very interesting approach, which starts from a "massive" QCD, is able to reproduce most, if not all, lattice results can be found in arxiv:1105.2475. They even can justify the presence of this mass from a certain form of gauge fixing. Worth to be read, in my opinion, but that's totally biased ;-)
Of course, the rigorous proof of "The mass of the least massive particle of the force field predicted by the theory is strictly positive" is still pending with a prize of US\$1,000,000. In comparison, a Lamborghini can start anywhere from \$200,000 to \\$500,000. So I am not particularly enthusiastic in telling ya the proof here at PSE.