Can the $\psi (4040)$ explain the peak associated with $Y(4008)$?

Abstract

We study the well-known resonance $\psi (4040)$, corresponding to a $3^3{S}_1$ charm-anticharm vector state $\psi (3S)$, within a QFT approach, in which the decay channels into $DD$, $D^{\ast }D$, $D^{\ast }{D}^{\ast }$, $D_s{D}_s$ and $D_s^{\ast }{D}_s$ are considered. The spectral function shows sizable deviations from a Breit-Wigner shape (an enhancement, mostly generated by $D{D}^{\ast }$ loops, occurs); moreover, besides the $c\bar{c}$ pole of $\psi (4040)$, a second dynamically generated broad pole at $4$ GeV emerges. Naively, it is tempting to identify this new pole with the unconfirmed state $Y(4008).$ Yet, this state was not seen in the reaction $e^{+}{e}^{-}\to \psi (4040)\to D{D}^{\ast }$, but in processes with ${\pi }^{+}{\pi }^{-}J/\psi$ in the final state. A detailed study shows a related but different mechanism: a broad peak at $4$ GeV in the process $e^{+}{e}^{-}\to \psi (4040)\to D{D}^{\ast }\to {\pi }^{+}{\pi }^{-}J/\psi$ appears when $D{D}^{\ast }$ loops are considered. Its existence in this reaction is not necessarily connected to the existence of a dynamically generated pole, but the underlying mechanism - the strong coupling of $c\bar{c}$ to \ $D{D}^{\ast }$ loops - can generate both of them. Thus, the controversial state $Y(4008)$ may not be a genuine resonance, but a peak generated by the $\psi (4040)$ and $D^{\ast }D$ loops with ${\pi }^{+}{\pi }^{-}J/\psi$ in the final state.

Comments: 16 pages, 6 figures, 2 tables