# Non-existence of gluon singlets: Any recent theoretical progress?

An unanswered question from last year (2012) on gluon singlets asked whether there is any theoretical explanation for the experimental absence of the ninth or colorless (singlet) gluon. This is the gluon that, if it existed, would give allow the strong force to extend far beyond the range of atomic nuclei, with catastrophic results. (Non-experts can find an explanation of the singlet gluon in the Addendum below.)

Qmechanic partially answered the question with a link to this 1996 paper by J.J. Lodder, which proposed that the singlet gluon exists but is so massive that its effects are negligible.

However, Lubber's massive-singlet idea seems to have gone nowhere. On an cursory search I could not find any references to the 1996 draft, even though it was written seventeen years. I also do not find Ludder's approach very plausible. Theoretically he had to do a bit of mayhem to Standard Model symmetries to come up with his model. More importantly, though, its seems unlikely that the idea holds water experimentally. The mass of the singlet gluon would have to be astronomical indeed for it not to have shown up in high-energy experimental results, especially in the post-Higgs era.

So, my version of the singlet question is this: Do there exist any plausible, Standard Model compatible theories for the observed absence of the singlet gluon, other than the apparently non-starter idea that the singlet exists but is very massive? Or alternatively, have searches for the Higgs boson produced any evidence that the singlet gluon state may in fact exist and have a very large mass?

Addendum for non-experts: What is a "gluon singlet" and why is it important?

One way to understand the "colorless" gluon singlet is through an analogy with how photons work for the electric force.

Photons interact with electrically charged electrons, but do not carry any electric charge themselves. Because they have no charge, even low-energy photons can easily escape an atom or electron and travel infinite distances. Imagine, however, what would happen if photons did carry electric charge. Such photons would have the same energetic difficulties leaving a neutral atom as an electron, dramatically altering and limiting how they behave. (I should probably mention that electrically-charged photons in one sense really do exist: They are more-or-less the $W^\pm$ particles of electroweak theory.)

Curiously, the charged situation is reversed for the otherwise photon-like gluons. It is the gluons that convey the strong force, and thereby hold quarks together to form protons and neutrons, as well as secondarily binding protons and neutrons together within atomic nuclei.

There are eight types of gluons instead of just one, due to there being more than two types of charge in the strong force. However, in sharp contrast to photons, all of the eight gluons normally carry strong (color) charge. The color charges of gluons cause them to interact strongly with the quarks that emit them and with each other. As in the earlier hypothetical example of how electrical charges would dramatically limit the range of photons, the presence of color charges on gluons similarly limits the distances over gluons can convey the strong force. Consequently, the strong force has almost no impact beyond the scale of atomic nuclei.

However, the same mathematical model that predicts the eight color-charged gluons also predicts a ninth neutral or strong-charge-free gluon, called the singlet gluon, that has never been seen experimentally. Its lack of color would make its impact far greater than that of any of the eight other gluons. In particular, just as charge-free photons can carry the electric force far beyond the range of atoms, a charge-free gluon, if it existed, would allow the strong force to extend far beyond the range of nuclei.

The repercussions would be huge. In fact, the non-existence of the singlet gluon is best demonstrated by the fact that we exist at all. My best guess (only that, since I have not seen any papers on it) is that if the colorless singlet quark really did exist, every clump of two or more atoms in the universe would melt together into an amorphous sea of quarks. Even if that is not correct, I assure you it that the consequences of the existence of singlet gluons would be... very bad indeed!

That is also why I find I think the non-existence of the singlet gluon is a truly interesting question, one that probably deserves more theoretical attention than it has received over the decades since strong force theory was first codified.