Abstract
We consider the interactions in a mesonic system, referred here to as ‘tetron’, consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally QaQbq¯cq¯d, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors Nc, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large Nc limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable bbu¯d¯ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.
Highlights
Multiquark hadrons, whose internal structure apparently goes beyond the standard template of three quark baryons and quark-antiquark mesons, have recently been observed in various experiments
All such exotic hadrons found so far contain a heavy b or c quark and a corresponding antiquark. For this reason they all are unstable with respect to annihilation of a heavy quark-antiquarks pair, even though their rate of dissociation into conventional hadrons can be small
In particular the most discussed models for the mesonic ones are the molecular [3, 2], the tetraquark and the ‘hadro-quarkonium’ [5, 6]
Summary
Multiquark hadrons, whose internal structure apparently goes beyond the standard template of three quark baryons and quark-antiquark mesons, have recently been observed in various experiments (for a recent review see e.g. [1, 2]). It appears that a stable tetron does not exist if the parameter ξ is of order one or larger It is plausible that the condition for existence of a stable tetron is a small value of the expansion parameter [in this model ξc in Eq (2)] describing the deviation from the point-like model for the pair of heavy constituents.
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