How does the $X(3872)$ show up in e⁺e⁻ collisions: dip versus peak

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⁻→ J/ψπ⁺π⁻ admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong S-wave D D^* attraction that generates the state $X(3872)$. We anticipate the appearance of a similar dip in the e⁺e⁻→ J/ψπ⁺π⁻π⁰ final state near the D^*D̄^* threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-two partner of the $X(3872)$.