How does the $X(3872)$ show up in $e^{+}{e}^{-}$ collisions: dip versus peak

Abstract

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong $S$-wave $D{\bar{D}}^{\ast }$ attraction that generates the state $X(3872)$. We anticipate the appearance of a similar dip in the $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ final state near the $D^{\ast }{\bar{D}}^{\ast }$ threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-two partner of the $X(3872)$.

4 pages, 2 figures; version to appear in Phys. Rev. D as a Letter