To investigate heavy quark systems (cc ̅ and bb ̅) using phenomenological inter-quark potentials we should use the non-relativistic framework because of their (cc ̅ and bb ̅) mass is above the relativistic limit. Firstly how can you proof it? and Second are they (cc ̅ and bb ̅) free particles?
The correct verb isn't ``should'', it's ``can'': the heavy quarkonium systems have properties, that *can* be described by treating them in the non-relativistic approximation, just like the hydrogen atom, only the potential doesn't have the same *meaning*.
The ``proof'' is that the calculated quantities can be compared to experiment and found to be consistent. It's not, just, that the mass of the quarkonia is ``large'', but, just like for the hydrogen atom, in the non-relativistic approximation, it is possible to identify degrees of freedom that move non-relativistically. There's been considerable work in lattice QCD-cf. http://arxiv.org/abs/1408.3003 for instance.
There has been, also, considerable work done on the mathematical properties of the quarkonia potentials, and it depends on what one is looking for. This is physics, however, so what really matters is that the approximations be clearly identified.
The J/ψ (the ccbar bound state) and the Υ (the bbbar bound state) are color singlets, so can appear as-unstable-particles in their own right-they aren't confined, any more than the pions are. The fact that they're unstable means that they can't be identified as free particles-they decay, so their properties are deduced from those of their decay products, the particles they decay into.
The correct verb isn't ``should'', it's ``can'': the heavy quarkonium systems have properties, that *can* be described by treating them in the non-relativistic approximation, just like the hydrogen atom, only the potential doesn't have the same *meaning*.
The ``proof'' is that the calculated quantities can be compared to experiment and found to be consistent. It's not, just, that the mass of the quarkonia is ``large'', but, just like for the hydrogen atom, in the non-relativistic approximation, it is possible to identify degrees of freedom that move non-relativistically. There's been considerable work in lattice QCD-cf. http://arxiv.org/abs/1408.3003 for instance.
There has been, also, considerable work done on the mathematical properties of the quarkonia potentials, and it depends on what one is looking for. This is physics, however, so what really matters is that the approximations be clearly identified.
The J/ψ (the ccbar bound state) and the Υ (the bbbar bound state) are color singlets, so can appear as-unstable-particles in their own right-they aren't confined, any more than the pions are. The fact that they're unstable means that they can't be identified as free particles-they decay, so their properties are deduced from those of their decay products, the particles they decay into.
Please try to find and to read these 2 volumes http://www.amazon.com/Dynamical-Groups-Spectrum-Generating-Algebras/dp/9971501473/ref=sr_1_1?ie=UTF8&qid=1462387597&sr=8-1&keywords=dynamical+groups+and+spectrum+generating+algebras
Following article demonstrates use of a relativistic spin dependent wave equation for analyzing heavy quarkonium system. The proof of the model is given by comparison of the model predictions with the laboratory measurement of energy levels of heavy quarkonium spectra. bb and cc are not free particles and this fact is reflected by the string tension parameter sigma in the Cornell potential.
Article Quarkonium and hydrogen spectra with spin-dependent relativi...
Many thanks Vikram. This is exactly the kind of paper I like, and myself I was recommending to read similar papers, e.g. see my comment.
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