Abstract
The state $\chi^{\vphantom\dagger}_{c0}(3915)$ has recently been demoted by the Particle Data Group from its previous status as the conventional $c\bar c$ $2 {}^3P_0$ state, largely due to the absence of expected $D\bar D$ decays. We propose that $\chi^{\vphantom\dagger}_{c0}(3915)$ is actually the lightest $c\bar c s \bar s$ state, and calculate the spectrum of such states using the diquark model, identifying many of the observed charmoniumlike states that lack open-charm decay modes as $c\bar c s \bar s$. Among other results, we argue that $Y(4140)$ is a $J^{PC} = 1^{++}$ $c\bar c s \bar s$ state that has been not been seen in two-photon fusion largely as a consequence of the Landau-Yang theorem.
Highlights
The past 13 years have been a time of remarkable growth in experimental reports of hadronic states, in the charmonium and bottomonium sectors
Based on interesting patterns in the phenomenology of the charmoniumlike states observed to date, we propose that the JPC 1⁄4 0þþ state χc0ð3915Þ is the lightest ccssstate
Its lack of observed DðÃÞDðÃÞ decays argue against it being either the conventional ccstate χc0ð2PÞ or a lightquark containing ccqqexotic state, and its single known decay mode J=ψω can be understood as the ω having a small sscomponent
Summary
The past 13 years have been a time of remarkable growth in experimental reports of hadronic states, in the charmonium and bottomonium sectors. The establishment of JPC 1⁄4 0þþ for χc0ð3915Þ immediately suggested that the state is the first radial excitation χc0ð2PÞ of the known conventional charmonium state χc0ð1PÞ, the 2P state mass being predicted in quark potential models to lie in the range 3842–3916 MeV [27,28,29]. A rather radical solution: The χc0ð3915Þ is a ccssstate, naturally an isosinglet that eschews open-charm decays It lies just below the Dþs D −s threshold (3937 MeV) as well as the J=ψφ threshold (4116 MeV), and the only OZI-allowed decay We assert that χc0ð3915Þ is the lightest ccssstate; the only lighter charmoniumlike exotic is Xð3872Þ, and it decays freely into open-charm states. Should it turn out to be a ccssstate, its χc0ω decay must proceed through the same ω-φ mixing or double-OZI suppression mechanism as suggested for χc0ð3915Þ
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