Abstract
The implementation of the heavy quark spin symmetry in possible molecular states at the mixed bottom-charm threshold is somewhat different from that at the open charm or bottom thresholds. In particular it depends on two parameters describing separately the symmetry for the bottom and for charmed quarks. The corresponding spin structures of the $S$-wave molecular states of the meson pairs $B^{(*)} D^{(*)}$ are discussed as well as their consequences for properties of possible near-threshold resonances, analogs of the known charmonium-like and bottomonium-like $X$ and $Z$ states.
Highlights
The implementation of the heavy quark spin symmetry in possible molecular states at the mixed bottomcharm threshold is somewhat different from that at the open charm or bottom thresholds
It can be noted that for the meson pairs with a hidden heavy flavor, i.e., DðÃÞDðÃÞ or BðÃÞBðÃÞ, there are additional implications for the heavy-light spin structure following from the charge symmetry for the neutral pairs, or from an approximate isospin symmetry for the charged ones
The C-even pair, e.g., D0D Ã0 þ D 0DÃ0, such as in the resonance Xð3872Þ, necessarily contains the heavy ccpair in the spin state Scc 1⁄4 1 and the light degrees of freedom have the total spin SL equal to one [9], SL 1⁄4 1, and the two total spins combine into the overall angular momentum J 1⁄4 1: D0D Ã0þD 0DÃ0∼ð1cc ⊗1LÞjJ1⁄41
Summary
The implementation of the heavy quark spin symmetry in possible molecular states at the mixed bottomcharm threshold is somewhat different from that at the open charm or bottom thresholds. The purpose of the present paper is to point out that some of the questions of molecular dynamics of heavy mesons can be studied in a somewhat different setting if in addition to charmoniumlike and bottomoniumlike states one could study mixed heavy flavor systems containing c quark and bantiquark.
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