Heavy-quark spin symmetry partners of the $X(3872)$ revisited

Understand

We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the $X(3872)$.

• We confirm that, if the $X(3872)$ were a $D\bar{D}^*$ molecular state with the quantum numbers $J^{PC}=1^{++}$, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the $X(3872)$, with the quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$ in line with previous results reported in the literature.
• We demonstrate that this result is robust with respect to the inclusion of the one-pion exchange interaction between the $D$ mesons.
• However, this is true only if all relevant partial waves as well as particle channels which are coupled via the pion-exchange potential are taken into account.