The heavy hadron spectrum is constrained by symmetries, of which two of the most important ones are heavy-quark spin and SU(3)-flavor symmetries. Here we argue that in the molecular picture the $Y(4230)$ [or $Y(4260)$], the $Y(4360)$, and the recently discovered $Y(4500)$ and $Y(4620)$ vectorlike resonances are linked by these two symmetries. By formulating a contact-range effective field theory for the $D{\overline{D}}_1$ and $D_s{\overline{D}}_{s1}$ family of $S$- and $P$-wave charmed meson-antimeson systems, we find that if the $Y(4230)$ were to be a pure $D{\overline{D}}_1$ molecular state, there would be a $D^{*}{\overline{D}}_1$ partner with a mass similar to the $Y(4360)$, a $D_s{\overline{D}}_{s1}$ partner with a mass close to the $Y(4500)$, and three $J=1$, 2 $D_s^{*}{\overline{D}}_{s1}$ and $J=3$ $D_s^{*}{\overline{D}}_{s2}^{*}$ bound states with a mass in the vicinity of 4630 MeV, of which the first one ($J=1$) might correspond with the $Y(4620)$. The previous predictions can in turn be improved by modifying the assumptions we have used to build the effective field theory. In particular, if we consider the closeness of the $D^{*}{\overline{D}}_1\text{−}{D}^{*}{\overline{D}}_2^{*}$ and $D_s^{*}{\overline{D}}_{s1}\text{−}{D}_s^{*}{\overline{D}}_{s2}^{*}$ thresholds and include the related coupled channel dynamics, we predict a $J=2$ positive $C$-parity state with a mass around 4650 MeV. This hidden-strange and hidden-charm state might in turn be identified with the $X(4630)$ that has been discovered during the past year by the LHCb in the $J/\psi \varphi$ invariant mass distribution.

• Received 16 June 2022
• Accepted 22 November 2022

DOI:https://doi.org/10.1103/PhysRevD.107.016001

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Published by the American Physical Society