Of course, this is a question of group theory. Glueballs are bound states of gluons, the eight particles that make up the adjoint representation of SU(3) color. So the quantum numbers of their bound states are determined from that fact.

Cf. for instance: http://arxiv.org/abs/1301.5183

http://pwa.hiskp.uni-bonn.de/talks/sarantsev_glueballs.pdf

Thanks Nicolis for your answer and ref.

All gluballs have color-singlet state or not?

Is it possible that

in gluon-gluon interactions some gluballs shows color state or some not?

You're welcome. Glueballs, insofar as they are states in the confining phase of QCD, are color singlets-that's what ``confining phase'' means. In the ``deconfined phase'', of course, nothing would prohibit the existence of color non-singlet states.

I would say that glueballs are a prediction of QCD. Since gluons are Yang-Mills fields, they interact with each other, in contrast with photons which do not interact directly. This means that gluons carry a charge named "color". But we know from experiments that the color charge is confined into hadrons. Then, glueballs should be white, or colorless states. This is possible by the addition of the three fundamental colors in the glueball. Another possibility for a colorless state is to have a particle with a color together with its antiparticle carrying the corresponding anticolor.

States of glueball consist of bound states of pure gluons. Gluons have color charge and therefore interact with each other. This leads to these vound states. Glueballs are a prediction of QCD and one signatire are non-natural parity-charge conjugation numbers (not being possible achieved by quark-antiquark or three quarks states.

We have dcetermined the clasification of many gluon states and the result can be deduced from one of my publications in 1999: P.O. Hess et al., "Glueball spectrum from an effective Hamiltionian", Eur. Phys. J. C 9 (1999), 121.

Thanks Boschi-Filho and Peter Hass for your answer.

The direct gluon-gluon coupling makes chromodynamics. We know that the gluon-gluon vertices are:- three-gluon vertices and four-gluon vertices. There are only eight gluon (bi-colored) in QCD. From these eight gluon, which gluons (their permutations) will be coupled and make the singlet state? It is possible that many gluons permutations show the color properties and many permutation shows color-singlet? i.e. dependent the gluon's colors?

In the publication I mentiones, there is a list of color singlet gluon state, up to six gluons. I have a program which determines for higher number of gluons and symmetries the color content, from which you can determine how many color singlet states are for a given number of gluons. If you are interested I can send it to you with some explanations.

Thanks to Peter Hass sir!

I am very interested for this topic. Please, provide me some data/matter related to my question.

Send an e-mail tomy address: [email protected]

I will send you a list of publications and some programs to determine the content of SU(3)-color states in an N-gluon system.

@ Peter Hass, I have send an email to your mail address, my e-mail address is: [email protected]

Please send me some publications related to SU(3)-color states of gluon interactions.

It is very hard to find a signature for glueball states so far one admit the existence of hybrid quark states. Anyway, a good general phenomenological rule is to search for glueball states in reactions that violate the Okubo-Zweir-Iizuka rule.

Experimentally one is looking for the glueball candidates in the reactions involving Pomeron - Pomeron fusion processes which are part of the central diffractive events (in p p collisions two protons emerge almost untouched). Pomeron itself is considered to be a purely gluonic object carrying the vacuum quantum numbers

(http://inspirehep.net/record/428117)