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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

This paper analyzes mechanisms of $D\bar{D}$ pair production in $e^+e^-$ and ultraperipheral heavy-ion collisions, concluding that the observed $D^0\bar{D}^0$ continuum bump originates from $t/u$ -channel exchanges rather than a resonance, while also characterizing the $\chi_{c2}(3930)$ as a candidate for the $\chi_{c2}(2P)$ state and providing branching fraction estimates and differential distributions for Belle II and LHC kinematics.

Original authors: Antoni Szczurek, Izabela Babiarz, Piotr Lebiedowicz, Wolfgang Schäfer

Published 2026-10-02

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CC BY 4.0

Original authors: Antoni Szczurek, Izabela Babiarz, Piotr Lebiedowicz, Wolfgang Schäfer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the subatomic world, matter is built from a small family of fundamental particles called quarks. When two quarks bind together, they form a particle known as a meson. Among these, the most famous are the charmonia, which are made of a charm quark and its antimatter partner, the charm antiquark. For decades, physicists have mapped out the "ground state" versions of these particles, much like knowing the basic notes on a piano. However, the excited versions—particles that vibrate with more energy—are far less understood. These excited states are crucial because they might hide new, exotic forms of matter that do not fit the standard rules of how quarks combine. To study them, scientists use particle colliders, smashing electrons and their antimatter counterparts, positrons, together. When these particles collide, they can briefly transform into pure energy, which then condenses into new particles, including pairs of heavy mesons. By watching how these new particles appear and interact, researchers can piece together the properties of the fleeting, excited states that created them.

A team of physicists led by Antoni Szczurek has taken a fresh look at how pairs of D mesons are produced in these electron-positron collisions. D mesons are a specific type of heavy particle containing a charm quark. The researchers focused on a particular puzzle: a broad, hump-shaped increase in the number of particle pairs observed at a specific energy level, around 3.8 billion electron volts. Previous observations by the Belle and BaBar collaborations had seen this bump in neutral D meson pairs but not in charged ones. Some had speculated that this bump was a new, broad resonance, a specific excited particle named $\chi_{c0}(3860)$ . The new study, however, suggests a different origin. By carefully calculating the background processes that occur when particles simply scatter off one another without forming a new resonance, the team found that this "bump" is likely just a natural fluctuation of the continuum, rather than evidence of a new particle.

The researchers built a detailed model to simulate two distinct ways these particle pairs can be created. The first is a resonant process, where the collision energy briefly forms a specific, short-lived particle before it decays into the final pair. The second is a continuum process, where the particles are produced directly through the exchange of other, heavier particles, without forming a distinct intermediate state. The team calculated the probabilities for both scenarios, paying close attention to the differences between neutral and charged D mesons. They found that for the neutral pairs, the continuum mechanism produces a significant signal that naturally creates a broad peak at the observed energy. For the charged pairs, this same mechanism produces a much smaller effect. This difference explains why the bump appears in one channel but not the other, supporting the idea that the feature is a background effect rather than a new particle.

The study also investigated a different excited state, the $\chi_{c2}(3930)$ , which is a strong candidate for a specific type of excited charmonium. The researchers compared their model predictions against experimental data to determine how often this particle decays into D meson pairs. By matching their calculations to the observed data, they estimated that about 58 percent of these particles decay into D meson pairs, with a margin of error of roughly 13 percent. This result helps refine our understanding of how these heavy particles behave and provides a clearer picture of the forces holding them together. The team also looked ahead to future experiments at the Large Hadron Collider, predicting that similar particle pairs could be produced in collisions between heavy lead ions, offering a new way to search for these rare states.

Ultimately, the work clarifies the landscape of heavy particle production. The broad enhancement at 3.8 billion electron volts, once a candidate for a new exotic particle, is now more likely to be understood as a complex interplay of standard particle exchanges. While the search for the true nature of the $\chi_{c0}(2P)$ state continues, the study provides a solid baseline for what the background looks like, ensuring that future discoveries are not mistaken for ordinary fluctuations. The findings underscore the importance of precise calculations in distinguishing between the noise of the continuum and the clear signal of a new resonance, guiding the next generation of experiments at facilities like Belle II.

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

Problem Statement
The paper addresses the production mechanisms of $D\bar{D}$ pairs in electron-positron collisions ( $e^+e^- \to e^+e^- \bar{D}D$ ) via two-photon fusion. A primary motivation is the interpretation of experimental data from the Belle and BaBar collaborations, specifically the observation of a broad enhancement at an invariant mass $M_{D\bar{D}} \approx 3.8$ GeV in the neutral $D^0\bar{D}^0$ channel, which is absent in the charged $D^+D^-$ channel. The authors aim to distinguish whether this structure arises from a broad resonance, tentatively identified as the excited P-wave charmonium state $\chi_{c0}(2P)$ (labeled $\chi_{c0}(3860)$ ), or from non-resonant continuum mechanisms. Additionally, the paper investigates the properties of the $\chi_{c2}(3930)$ resonance, a candidate for the $\chi_{c2}(2P)$ state, and extends the analysis to ultraperipheral heavy-ion collisions (UPCs) at the LHC.

Methodology
The authors perform calculations for the exclusive $2 \to 4$ reaction $e^+e^- \to e^+e^- \bar{D}D$ using the Equivalent Photon Approximation (EPA) for small-angle lepton scattering. The total cross-section is derived by integrating the squared amplitude over an eight-dimensional phase space. The amplitude is decomposed into two distinct production mechanisms:

Continuum Production:
- Neutral Channel ( $D^0\bar{D}^0$ ): Modeled via $t$ - and $u$ -channel exchanges of the vector meson $D^*(2007)^0$ . The $D^*D\gamma$ coupling constants are derived from experimental $D^* \to D\gamma$ decay widths. The vector meson propagators are treated with Reggeization effects.
- Charged Channel ( $D^+D^-$ ): Modeled primarily via $t$ - and $u$ -channel exchanges of the pseudoscalar $D^\pm$ mesons, supplemented by a contact term. The $D^*(2010)^\pm$ exchange is also considered as a sub-dominant mechanism.
- Form Factors: Off-shell effects are accounted for using form factors dependent on photon virtualities ( $Q^2$ ) and meson momenta. Parameters for these form factors (e.g., $\Lambda_{D^*}$ ) are fitted to experimental data.
Resonant Production:
- The process proceeds through intermediate $s$ -channel resonances: $\chi_{c0}(3860)$ and $\chi_{c2}(3930)$ .
- $\chi_{c2}(3930)$ : Assumed to be the $\chi_{c2}(2P)$ state with a pure $c\bar{c}$ component. The two-photon coupling is calculated in the Non-Relativistic QCD (NRQCD) limit using the Buchmüller-Tye (BT) and Cornell potentials. The decay width to $D\bar{D}$ is constrained by isospin invariance.
- $\chi_{c0}(3860)$ : Two scenarios for the mass and total width ( $\Gamma$ ) are tested: one with a large width ( $\Gamma \approx 200$ MeV) based on PDG averages, and a narrower scenario ( $\Gamma = 50$ MeV).

The model results are compared against experimental differential distributions and invariant mass spectra from Belle and BaBar. The analysis also includes predictions for ultraperipheral Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.

Key Contributions and Results

Continuum vs. Resonance in $D^0\bar{D}^0$ : The authors find a relatively large continuum contribution for the $D^0\bar{D}^0$ channel, which peaks around 3.8 GeV. In contrast, the continuum contribution for the $D^+D^-$ channel is significantly smaller. The model suggests that the broad bump observed at $M_{D^0\bar{D}^0} \approx 3.8$ GeV is primarily of continuum origin rather than a manifestation of a broad $\chi_{c0}(3860)$ resonance.
$\chi_{c2}(3930)$ Properties: The $\chi_{c2}(3930)$ is identified as a strong candidate for the $\chi_{c2}(2P)$ state. By comparing the model's prediction for the two-photon width $\Gamma(\chi_{c2}(2P) \to \gamma\gamma) = 0.544$ keV (derived from the BT potential) with BaBar data, the authors extract the branching fraction:
$B(\chi_{c2}(3930) \to D\bar{D}) = 0.58 \pm 0.13$
(using the BT potential). A value of $0.38 \pm 0.08$ is obtained using the Cornell potential.
$\chi_{c0}(3860)$ Interpretation: The analysis indicates that assuming a narrow width ( $\Gamma_{\chi_{c0}} = 50$ MeV) improves the description of near-threshold data, particularly for the BaBar $D^+D^-$ channel. Conversely, the scenario with a large width ( $\Gamma_{\chi_{c0}} \approx 200$ MeV) leads to a surprisingly small branching fraction $B(\chi_{c0} \to D\bar{D})$ and a poorer description of the low-mass data. The authors note the difficulty in reconciling a large total width with the observed partial width to $D\bar{D}$ .
Interference Effects: Significant interference is observed between the $\chi_{c0}(3860)$ resonance and the $D^0\bar{D}^0$ continuum, as well as between the $\chi_{c2}(3930)$ and the continuum.
Heavy-Ion UPCs: The paper presents predictions for exclusive $D\bar{D}$ production in Pb-Pb collisions at the LHC for low invariant masses ( $M_{D\bar{D}} < 4.3$ GeV). The calculated nuclear cross-sections are approximately 115 $\mu$ b for $D^0\bar{D}^0$ and 30 $\mu$ b for $D^+D^-$ (with specific kinematic cuts).

Significance and Claims
The paper claims to provide a comprehensive description of $e^+e^- \to e^+e^- \bar{D}D$ data by simultaneously modeling continuum and resonant contributions. The primary conclusion is that the broad enhancement at 3.8 GeV in the neutral channel is likely a continuum effect, challenging the interpretation of this structure solely as a broad $\chi_{c0}(2P)$ resonance. The work provides a quantitative extraction of the branching fraction for $\chi_{c2}(3930) \to D\bar{D}$ and highlights the need for further theoretical and experimental research to clarify the properties of the $\chi_{c0}(2P)$ state.

The authors modestly suggest that their results motivate a more detailed analysis of $D\bar{D}$ production, which they anticipate will be feasible with future high-statistics data from the Belle II experiment. They also propose that ultraperipheral heavy-ion collisions at the LHC offer a complementary environment to search for light exotic charmonium states and study open-charm meson pair production, potentially providing new information distinct from $e^+e^-$ collider data.

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