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 $γγ\to D \bar{D}$ subprocess is done including the continuum mechanisms and the $χ_{c0}(3860)$ and $χ_{c2}(3930)$ resonant contributions. These states are considered as candidates for the first excited $P$-wave charmonia $χ_{c0}(2P)$ and $χ_{c2}(2P)$. We compare our results for the $γγ\to D \bar{D}$ 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 $μ$b and 29 $μ$b, respectively, taking into account the cuts on pseudorapidities and transverse momenta of the final state charmed mesons ($|η_{D}| < 2.5$, $p_{t,D} > 0.2$ 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 ${\rm Pb} {\rm Pb} \to {\rm Pb} {\rm Pb} (γγ\to χ_{c0,2}(2P) \to D \bar{D})$ 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.

Figures (4)

• Figure 1: Diagram representing $D^{+}D^{-}$ production in ultraperipheral $\rm Pb$-$\rm Pb$ collisions. For the $\gamma \gamma \to D^{+} D^{-}$ process we consider the $t$- and $u$-channel $D^{\pm}$ and $D^{*}(2010)^{\pm}$ exchanges, the contact term, and the $s$-channel $\chi_{c0}$ and $\chi_{c2}$ exchanges. The diagrams for the $D^0 {\bar{D}}^0$ production are similar, but in the case of continuum mechanism we consider only the $D^{*}(2007)^{0}$$t/u$-channel exchanges.
• Figure 2: The differential cross sections for the $\gamma \gamma \to D \bar{D}$ processes and comparison of theoretical results with the Belle Belle:2005rte and BaBar BaBar:2010jfn data. The theoretical results for the complete model (continuum, $\chi_{c0}(3860)$, and $\chi_{c2}(3930)$ contributions) and for the continuum contribution alone are shown. The red long-dashed lines correspond to the $D^0 {\bar{D}}^0$ channel and the blue dashed lines correspond to the $D^{+}D^{-}$ channel. The black solid line represents the sum of all contributions for the two channels.
• Figure 3: The differential nuclear cross sections for the reactions ${\rm Pb}{\rm Pb} \to {\rm Pb}{\rm Pb} D^{0} \bar{D}^{0}$ (the red band) and ${\rm Pb}{\rm Pb} \to {\rm Pb}{\rm Pb} D^{+}D^{-}$ (the blue dotted curve) calculated for $\sqrt{s_{NN}} = 5.02$ TeV and imposing cuts: $|\eta_{D}| < 2.5$, $p_{t,D} > 0.2$ GeV, and $M_{D \bar{D}} < 4.3$ GeV. For the $D^{0} \bar{D}^{0}$ channel, the continuum contribution was calculated for $\Lambda_{D^{*0}} = 3.3$ and 3.5 GeV in (\ref{['DstarDgam_ff_exp']}), which corresponds to the lower and upper red long-dashed lines in the bands, respectively.
• Figure 4: The distribution in $D^{0} \bar{D}^{0}$ invariant mass for the ${\rm Pb}{\rm Pb} \to {\rm Pb}{\rm Pb} D^{0} \bar{D}^{0}$ reaction. The calculations were done for $\sqrt{s_{NN}} = 5.02$ TeV, $|\eta_{D}| < 2.5$ and $p_{t,D} > 0.2$ GeV. The result for the continuum contribution corresponds to $\Lambda_{D^{*0}} = 3.5$ GeV.