Abstract
We discuss the adequate treatment of the 3- and 4-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be rather misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.
Highlights
There is rich literature on multiquarks, and many reviews, including [1]
The sector of flavor-exotic tetraquarks was somewhat forgotten, and even omitted from some reviews on exotic hadrons, as much attention was paid to hidden-flavor states QQqq
Variational methods have been applied from the beginning of quantum mechanics, as they were already used in other fields of physics involving similar equations
Summary
There is rich literature on multiquarks, and many reviews, including [1]. The wave function contains a single color configuration, while in other papers the role of color mixing is analyzed. We stress that a careful treatment of the few-body problem is required before drawing any conclusion about the existence of stable states in a particular model. Some authors who use similar ingredients obtain either stability or instability for the all-heavy configuration QQQ Q , and in our opinion, this is because of an erroneous handling of the four-body problem in some papers.
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