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From Wikipedia Glueballs

Glueballs are predicted by quantum chromodynamics to be massive, notwithstanding the fact that gluons themselves have zero rest mass in the Standard Model. Glueballs with all four possible combinations of quantum numbers P (parity) and C (c-parity) for every possible total angular momentum have been considered, producing at least fifteen possible glueball states including excited glueball states that share the same quantum numbers but have differing masses with the lightest states having masses as low as 1.4 GeV/c2 (for a glueball with quantum numbers J=0, P=+, C=+), and the heaviest states having masses as great as almost 5 GeV/c2 (for a glueball with quantum numbers J=0, P=+, C=-).

Rather than going through a list of possible mechanisms that unfortunately I know next to nothing about, such as can the mass be attributed to virtual quarks, or binding energy between the gluons, I would rather leave the question as in the title to find out as much as I can.

Also, although the SM is firmly established, would the discovery of Glueballs buttress it further?

My apologies for not knowing more about the interior of hadron like particles or if the answer is readily available (or worse, blindingly obvious).

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If you had a gas of photons in a perfect cavity and these photons had energy $E~=~h\nu$, then for $N$ photons the cavity would have a mass $m~=~Nh\nu/c^2$ of photons. Glueballs as similar. The gluon carries two color charges (really color plus anti-color) and they can interact with each other. This forms a self-bound system that confines the massless gauge bosons.

In the glueball the gluons are not virtual particles. They have been generated by energy input in much the same way photons are generated. However, since they couple to each other they have this self-binding property the holds their mass-energy in a localized region of space. This gives the glueball a net mass. The situation with a hadron is more subtle. Quarks are bound by gluons, and the gluons also bind to each other. While the gluons are virtual, they define a vacuum bubble that has much higher energy than the region outside the bubble. From the perspective of an outside observer, this hadron then has a net mass that is considerably larger than the mass of the quarks.

This forms a part of the mass-gap problem. Nonabelian gauge fields that interact with themselves can form self-bound structures that have a net mass. This is in QCD a renormalization group problem at the low energy and strong coupling limit. This is difficult to understand, and largely I thing progress in this area has been with lattice gauge QCD done numerically. The mass-gap problem is an outstanding problem at Claymath.

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Because in relativity the mass of a collection of particles is not necessarily the sum of the masses.

Even two photons (treated as a unit) can have mass. Consider the total four-vector of a system with component four-vectors $(E,\hat{z}E/c)$ and $(E,-\hat{z}E/c)$. It has mass $(mc^2)^2 = (2E)^2$.

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  • $\begingroup$ Maybe there is also a reason, that the gluons, being also (strongly) charged, have a potential energy in the field of the other gluons? $\endgroup$
    – peterh
    Jul 9, 2016 at 23:37
  • $\begingroup$ @peterh Yeah. And confinement means the system will remain compact which is certainly not the case with my two photons unless you stick them in a mirror box. $\endgroup$ Jul 9, 2016 at 23:39
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    $\begingroup$ The existence of the pi0 which decays to two massless photons is a good example for this , $\endgroup$
    – anna v
    Jul 10, 2016 at 3:55
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Because glueballs have energy, and $E = m c^2$ says that energy is equivalent to mass. (Or another way to say it is that if you "zoom out" far enough that you can't see the constituent gluons that form the glueball, than you just lump all their energy into an effective glueball mass.) The energy can be thought of as just being the kinetic energy of the individual gluons, which are zooming around each other at highly relativistic speeds. (Strictly speaking, it's actually less than the sum of the individual gluon kinetic energies, because you have to subtract off the strong-force binding energy that holds the glueball together.)

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