Interference effect as resonance killer of newly observed charmoniumlike states $Y(4320)$ and $Y(4390)$

Abstract

In this letter, we decode the newly observed charmoniumlike states, $Y(4320)$ and $Y(4390)$, by introducing interference effect between $ψ(4160)$ and $ψ(4415)$, which plays a role of resonance killer for $Y(4320)$ and $Y(4390)$. It means that two newly reported charmoniumlike states are not genuine resonances, according to which we can naturally explain why two well-established charmonia $ψ(4160)$ and $ψ(4415)$ are missing in the cross sections of $e^+e^- \to π^+ π^- J/ψ$ and $π^+ π^- h_c$ simultaneously. To well describe the detailed data of these cross sections around $\sqrt{s}=4.2$ GeV, our study further illustrates that a charmoniumlike structure $Y(4220)$ must be introduced. As a charmonium, $Y(4220)$ should dominantly decay into its open-charm channel $e^+e^- \to D^0 π^+ D^{\ast-}$, which provides an extra support to $ψ(4S)$ assignment to $Y(4220)$. In fact, this interference effect introduced to explain $Y(4320)$ and $Y(4390)$ gives a typical example of non-resonant explanations to the observed $XYZ$ states, which should be paid more attention especially before identifying the observed $XYZ$ states as genuine resonances.