Exclusive $D \bar{D}$ pair production with low invariant mass in ultraperipheral Pb-Pb collisions at the LHC

Abstract

We present predictions for the ultraperipheral heavy-ion reaction ${\rm Pb} {\rm Pb} \to {\rm Pb} {\rm Pb} D \bar{D}$, where $D$ refers to either $D^0$ or $D^+$, limiting to low invariant mass of $D \bar{D}$ and at energies available at the LHC. The calculation of the $\gamma \gamma \to D \bar{D}$ subprocess is done including the continuum mechanisms and the $\chi_{c0}(3860)$ and $\chi_{c2}(3930)$ resonant contributions. These states are considered as candidates for the first excited $P$-wave charmonia $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$. We compare our results for the $\gamma \gamma \to D \bar{D}$ process with the $D \bar{D}$ invariant mass and angular distributions measured by the Belle and BaBar experiments in $e^{+}e^{-}$ collisions. Then, we present first calculations for ultraperipheral Pb-Pb collisions (UPCs) within the equivalent photon approximation in the impact-parameter space. Both, the total cross section and several differential distributions for experimental cuts corresponding to the ALICE, ATLAS, CMS, and LHCb experiments are presented. For instance, the nuclear cross sections for the $D^{0} \bar{D}^{0}$ and $D^{+} D^{-}$ channel at $\sqrt{s_{NN}} = 5.02$ TeV are found to be approximately 100--132 $\mu$b and 29 $\mu$b, respectively, taking into account the cuts on pseudorapidities and transverse momenta of the final state charmed mesons ($|\eta_{D}| < 2.5$, $p_{t,D} > 0.2$ GeV) and for $M_{D \bar{D}} < 4.3$ GeV. Results for $\sqrt{s_{NN}} = 5.36$ TeV are also presented. Cross section for the ${\rm Pb} {\rm Pb} \to {\rm Pb} {\rm Pb} (\gamma \gamma \to \chi_{c0,2}(2P) \to D \bar{D})$ processes is sufficiently large for experimental studies. The back-to-back correlation between charm mesons can be used to separate the exclusive process under consideration from other background processes, and could provide valuable insight into the properties of the excited quarkonia.