It is known that QED does not have a mass gap.

On the other hand, at the heuristic level, QCD has a mass gap.

But photons and gluons are both "massless". Could anyone explain (at least at the conceptual level) what the fundamental difference between gluons and photons is?

  • $\begingroup$ The fundamental difference is that QED is infrared-free and QCD is ultraviolet-free. This is explained in any textbook that discusses beta functions. $\endgroup$ Commented Dec 7, 2022 at 21:08
  • $\begingroup$ I know this fact but it does not seem to be related to issue of mass gap that much.. $\endgroup$
    – Keith
    Commented Dec 8, 2022 at 18:23
  • $\begingroup$ it is related very much. The mass gap is a property of the far infrared. Infrared-freedom means that interactions are turned off at low energies, thus you can use the free theory (which has a mass gap if and only if the electron is massive). For ultraviolet-free theories interactions are strong in the infrared, and the free theory is useless at low energies. $\endgroup$ Commented Dec 15, 2022 at 17:41

1 Answer 1


The difference is gluons carry their own charge and thus are bound in glueballs, and while gluons are massless, glueballs are not. It is glueballs, not gluons, which give a mass gap.

  • $\begingroup$ This is wrong. In 2d, photons do not carry their own charge but they still generate a mass gap (cf. the Schwinger model). And in 4d, if you add enough fermions, the theory becomes gapless regardless of whether gluons carry their own charge or not (cf. the conformal window). $\endgroup$ Commented Dec 7, 2022 at 21:07
  • $\begingroup$ @AccidentalFourierTransform I might change my answer to focus on confinement, which is shared with Schwinger photons, rather than the QCD-specific reason for it. Unfortunately, I can't find any details on how the conformal window does what you say; could you explain it? $\endgroup$
    – J.G.
    Commented Dec 7, 2022 at 21:23
  • $\begingroup$ I have no idea what confinement means ;-) $\endgroup$ Commented Dec 7, 2022 at 21:26
  • $\begingroup$ Sorry, I don't see how that covers it. $\endgroup$
    – J.G.
    Commented Dec 7, 2022 at 21:40
  • $\begingroup$ I am the OP in that post. I was just making the point that I don't know what confinement means, so I cannot explain whether it is there in the conformal window or not. $\endgroup$ Commented Dec 7, 2022 at 21:46

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