Earlier questions under a similar title referred to the short range of the strong force. My question is completely different. I'd like to know why gluons are considered massless in the Standard Model (regardless of the range of the strong force). For example, if mass is a result of the Higgs interactions, then why do gluons not interact with the Higgs boson? In addition to the theoretical reasons, is there any experimental evidence of gluons being actually massless? (I do realize that such experiments are not easy, because of the confinement.)
In the past, neutrinos were also considered massless, but not anymore. Is there a similar possibility for gluons to have perhaps a small invariant mass or is there an overriding reason for them to be definitely massless?
EDIT: The answer I've been looking for is deep in the comments below and not immediately apparent. To make it clear, I am repeating it here: To interact with a boson, a particle (the Higgs) must have a charge mediated by this boson. The Higgs has a weak charge and therefore interacts with the W and Z bosons thus giving them mass. The Higgs does not have the electric or color charge and therefore does not interact with the photon or gluons thus leaving them massless.
Best Answer
Simply put, the Higgs isn't charged under the strong force. It doesn't have standard electrical charge either. The $W^{\pm},Z$ bosons aquire a mass through the Higgs mechanism because the Higgs itself is charged under the weak force. Leptons aquire masses through the Higgs mechanism because they too interact with the Higgs.
No Higgs interaction means no effective mass.
You ask why the Higgs does not interact with gluons. It has to do with the quantum numbers (charges) of the fundamental particles in the standard model. It turns out that you aren't allowed to freely choose quantum numbers for the different particles. If you made a bad choice, you'd violate gauge invariance and have an inconsistent theory. This puts relatively strict constraints on the allowed quantum numbers. check out Gauge Anomaly for more details.
Basically, the known quantum numbers of the other standard model particles constrains the allowed quantum numbers of the Higgs, specifically prohibiting a gluon-higgs interaction. if you wanted to add that interaction, you would necessarily imply the existence of other particles in order to balances all the charges of the theory. I don't know if that would be possible, but its a matter of simple algebra to figure it out.