MathematicalPhysicist said:
According to wikipedia, they are only candidates not a definitive detection.
I wonder when will they become definitive? and how do they become definitive?
One of the very first things calculated with QCD once it was invented in the last 1970s and early 1980s were the complete set of properties of the pure glueball resonances in their ground states. This is because the calculation of a glueball resonance is less dependent upon experimentally measured physical constants of the Standard Model in addition to the strong force coupling constant, than those of any other hadron which dependents upon the strong force coupling constant and other Standard Model physical constants already at tree-level, making the complications much more difficult to make. Another benefit of present in doing these calculations is that they have a higher degree of symmetry than many QCD calculations.
Those calculations have since been refined to higher precision with more loops included in the calculations as more effort and more computational power has become available.
Since then, we've observed the physically existing resonances in those mass ranges for the quantum numbers that different kinds of glueballs would have to have close to comprehensively, and have not seen the predicted pure glueball resonances. This is because the energies necessary to form a glueball, in theory, at least, are far smaller than the energies of, for example, the Large Hadron Collider, or the formerly active Tevatron collider at Fermilab. So, we infer that in physical reality, glueball resonances are almost always mixed with non-glueball hadron states.
As a result, the best one can hope for, realistically, is a description of some hadron resonances that are "perfectly" explained by a specific glueball resonance mixed with other non-glueball hadron resonances, in a way that can be post-dicted from the examples giving you the insight to other examples that weren't used directly to generate the prediction.
Since we can explain almost all baryons and pseudo-scalar and ordinary vector mesons properties with little or no invocation of glueball elements, realistically, glueballs are primarily observed in mixes that give rise to some scalar mesons and axial vector meson resonances (which don't have ready explanations in an oversimplified constituent quark model that is sufficient to describe the spectrum of ground states of other hadrons which we observe).
The Jefferson Labs in Newport News, Virgina's
GlueX experiment has the research program most focused on this particular problem right now. The recent papers and conference talks from members of the collaboration linked
here are a good way to understand the state of the research on this question.
