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

Abstract

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 $t/u$-channel $D^*$ vector-meson exchanges, where the $D^* D γ$ coupling constants are derived from the $D^* \to D γ$ 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 $χ_{c0}(3860)$ resonance. We also investigate the resonant production of $D \bar{D}$ pairs, including $χ_{c0}(3860)$ and $χ_{c2}(3930)$. The $χ_{c2}(3930)$ meson is a good candidate for the first excited $P$-wave charmonium $χ_{c2}(2P)$ 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 $Γ(χ_{c2}(2P) \to γγ) = 0.544$ keV (corresponding to the Buchmüller-Tye potential) to the BaBar data, we find $B(χ_{c2}(3930) \to D \bar{D}) = 0.58 \pm 0.13$. We present results for differential distributions in several variables for Belle II kinematics. Finally, we shortly mention predictions for the ultraperipheral heavy-ion reaction $Pb Pb \to Pb Pb D \bar{D}$ for low invariant mass ($M_{D \bar{D}} < 4.3$ GeV) at the LHC.