# Why are gluons massless as their range is finite?

The range of electromagnetic waves and gravitational force is infinity and the particles exchanged during these interactions are photons and gravitons respectively. Both are massless following the relation: the range is inversely proportional to why.

Then why are the intermediating particle (gluons) massless in strong interactions (as their range is in fermi)?

• One can think about the strong interaction range in reverse: not only its range is infinite, but it also does not weaken at a distance the way gravity and electromagnetic do. The energy of the interaction grows with the distance and this makes the interaction irrelevant at a distance where the energy gets enough to create a pair of new quarks. Aug 27, 2023 at 13:59

The important difference is: gluons are charged (carrying color charge and anti-color charge, e g. $$r\bar b$$) while photons are not charged (zero electric charge). The resulting gluon-gluon interactions make it effectively a short-range interaction in spite of the gluon mass being zero. In contrast to this there are no photon-photon interactions, and that is why photons can propagate infinitely far.

Quoted from Gluon - Confinement:

Since gluons themselves carry color charge, they participate in strong interactions. These gluon–gluon interactions constrain color fields to string-like objects called "flux tubes", which exert constant force when stretched. Due to this force, quarks are confined within composite particles called hadrons. This effectively limits the range of the strong interaction to $$1\times 10^{−15}$$ meters, roughly the size of a nucleon.

• Photon-photon interaction does not exist in tree level, but does exist in higher orders (e.g. electron-loop). Aug 12, 2023 at 13:47
• @RdBasha you are correct, I oversimplified it a little bit on purpose. Aug 12, 2023 at 21:03
• But shouldn't this same caveat apply to gravity and gravitons as well? Gravitons are presumed massless, but nonetheless have energy (and under GR all particles are affected by gravity). So, shouldn't that also make gravity short-range? Aug 13, 2023 at 13:11
• @RBarryYoung the fact that no theory that includes gravitons actually works may have something to do with it. Aug 13, 2023 at 14:23
• "The gluon is massive": this paper (1987) seems to indicate that the gluon propagator, computed using lattice calculations, resembles that of a massive particle $\sim$ 600 MeV. Aug 14, 2023 at 1:20

Other people correctly answered how, although gluons are massless, their range appears to be very short. This happens because unlike photons, gluons have (color) charge, and therefore interact among themselves, and create color confinement.

A separate question is why are gluons massless. Well, all gauge bosons - photons, W/Z bosons, gluons, all start out massless. Higgs mechanism causes the symmetry in the Higgs field to generate excitations ("Goldstone bosons") which merge with some of the massless gauge bosons to create new particles - the W/Z vector bosons (massive), the photon (massless) and the Higgs scalar boson (massive). The gluons are unchanged by this mechanism (they do not have electric or weak charges, so they don't interact with the Higgs field), so they remain massless.

I do not think photons or gravitons are massless because their range is infinite, this is not the reason, rather consequence of lack of self interactions between them. Conversely $$SU(3)$$ gauge theory has immediate consequence of self interactions between gluons and confinement. The massless nature is coming from the $$SU(3)$$ and lack of presence of mass generation mechanisms. This is same for any $$U(N)$$ gauge thoery.

• I don't think this is entirely correct, gravity can self-interact. See this answer on self-interacting gravity physics.stackexchange.com/a/643784/231892 and others in there as well. Furthermore, EM is linear (no self-interaction) while gravity is inherently non-linear (self-interacting). Aug 13, 2023 at 18:44
• Tachyon, I think you're correct, but I think that if you consider the low-energy cases, the self-interaction of gravity is low (a low-energy gravity wave effects gravity minimally because it has low energy), but the self-interaction of low-energy gluons is still important (the gluon's effect on other gluons depends on its fixed color charge, which is unrelated to the amount of energy it carries). Aug 14, 2023 at 5:21