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.
|Original language||English (US)|
|Number of pages||6|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - Mar 10 2018|
Bibliographical noteFunding Information:
We thank Mariusz Puchalski for sharing his unpublished code for variational calculations. We thank Connor Stephens for collaboration at an early stage of the project. The research of A.C. and B.L. was supported by the Natural Sciences and Engineering Research Council ( NSERC ) of Canada, and by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence Origin and Structure of the Universe . B.L. is supported by the Canadian Institute for Nuclear Physics Undergraduate Research Scholarship . The work of M.B.V. is supported in part by U.S. Department of Energy Grant No. DE-SC0011842 . Appendix A