Mechanisms of $D\bar{D}$ pair production in $e^{+}{e}^{-}\to e^{+}{e}^{-}D\bar{D}$ and $AA\to AAD\bar{D}$ reactions and production of exotic charmonia

We discuss mechanisms of $D\bar{D}$ pair production in $e^{+}{e}^{-}$ collisions. We consider the $D^0{\bar{D}}^0$-continuum mechanism with the $t\mathrm{/}u$-channel $D^{\ast }$ vector-meson exchanges, where the $D^{\ast }D\gamma$ coupling constants are derived from the $D^{\ast }\to D\gamma$ decays. For the $D^{+}{D}^{-}$ channel, we consider mainly the $D^{\pm }$ exchanges. We find a relatively large continuum contribution for the $D^0{\bar{D}}^0$ channel and a significantly smaller one for $D^{+}{D}^{-}$, concluding that the broad bump at $M_{D^0{\bar{D}}^0}=3.8$ GeV observed by the Belle and BaBar Collaborations has a continuum origin rather than corresponding to the broad ${\chi }_{c0}(3860)$ resonance. We also investigate the resonant production of $D\bar{D}$ pairs, including ${\chi }_{c0}(3860)$ and ${\chi }_{c2}(3930)$. The ${\chi }_{c2}(3930)$ meson is a good candidate for the first excited $P$-wave charmonium ${\chi }_{c2}(2P)$ state. This resonance can decay into both $D\bar{D}$ channels; however, its branching fractions are not well known at present. Comparing our model result with $\mathrm{\Gamma }({\chi }_{c2}(2P)\to \gamma \gamma )=0.544$ keV (corresponding to the Buchmüller-Tye potential) to the BaBar data, we find $B({\chi }_{c2}(3930)\to D\bar{D})=0.58\pm 0.13$. We present results for differential distributions in several variables for Belle II kinematics. Finally, we shortly mention predictions for the ultraperipheral heavy-ion reaction $PbPb\to PbPbD\bar{D}$ for low invariant mass ($M_{D\bar{D}}<4.3$ GeV) at the LHC.