Abstract
This paper focuses on tetraquarks containing one heavy quark and one heavy antiquark in the formal limit where the heavy quark masses go to infinity. It extends the theoretical framework developed for tetraquark containing two heavy quarks based on semi-classical analysis and the Born-Oppenheimer approximation. It is shown that for sufficiently small light quark masses, parametrically narrow $q\bar{q}'Q\bar{Q}$ tetraquarks must exist in the formal limit of arbitrarily large heavy quark masses. The analysis is model-independent; it requires no assumptions about the structure of the state or the mechanism of its decay beyond what can be deduced directly from QCD. The formal analysis here is only directly applicable to tetraquarks with large angular momentum and hence does not directly apply to experimentally observed tetraquark candidates. We also discuss the condition needed for a version of the analysis to apply for low angular momenta states. Whether this condition holds can be explored via lattice calculations. Current lattice calculations suggest that the condition is not met. If these preliminary calculations are confirmed, there are strong implications for the nature of the observed tetraquark resonances containing $\bar{c}c$ or $\bar{b}b$ pairs. It raises the possibility that the observed tetraquarks exist and are narrow not because the charm and bottom quarks are extremely heavy, but because they are sufficiently light.
Highlights
Understanding exotic hadrons is an important branch of the current hadron structure and spectroscopy research
This paper focuses on exotic hadrons containing one heavy quark Q and one heavy antiquark Qin the formal limit where the heavy quark masses are taken to be arbitrarily large
The section discusses conditions that allow one to extend the previous work on qq 0QQ to qq 0QQtetraquark in a simple way. This will occur if the BornOppenheimer-type wave function that emerges from the analysis is effectively confined to a region in space in which the two heavy quarks are sufficiently far from each other, so that rearrangement effects that violate underlying assumptions of the analysis are suppressed. Following this a key argument will be shown: for sufficiently large heavy quark masses that allow a Born-Oppenheimer description at large distances and sufficiently small light quark masses, there always exists a range of angular momenta for which the Born-Oppenheimer effective potential in a channel with isospin one qq 0QQtetraquark quantum numbers will have a local minimum with the quarks separation of order m−π 1
Summary
Understanding exotic hadrons is an important branch of the current hadron structure and spectroscopy research. It was observed that, for very large heavy quark masses, there are numerous such tetraquark states with given quantum numbers and the higher-lying ones of these are not stable against strong decays [21]— they can decay via pion emission into lighter tetraquarks Such unstable states were shown to be parametrically narrow; the resonances become increasingly discernible as the heavy quark limit is approached. It is shown in a model-independent way that exotic tetraquarks of the QQtype must exist as parametrically narrow resonances in the formal heavy quark limit—at least if the pion is sufficiently light. Though the artificial limit where the heavy quark mass is arbitrarily large is not well satisfied in the real world, and tetraquarks with large angular momenta are not directly
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