Competition of $\chi_{c}(2P)$ quarkonia and continuum in $e^+ e^- \to e^+ e^- D \bar{D}$

TL;DR

This paper analyzes the production mechanisms of D meson pairs in electron-positron collisions, examining continuum contributions and resonance effects, and compares theoretical predictions with experimental data to clarify the nature of observed structures.

Contribution

It provides a detailed model of D meson pair production considering continuum and resonance contributions, and offers insights into the nature of the 3.8 GeV bump and the properties of the χc2(3930) state.

Findings

The 3.8 GeV bump is likely a continuum effect, not a broad resonance.

The χc2(3930) branching fraction to D D̄ is approximately 58%.

Predictions for differential distributions match experimental data within uncertainties.

Abstract

We discuss the production of $D \bar{D}$ pairs in $e^+ e^-$ collisions, where $D$ refers to either $D^0$ or $D^+$. The continuum mechanism with the $t/u$-channel vector-meson $D^*$ exchanges are considered. The results of the calculation depend on the parameter of the off-shell form-factor for the virtual $D^*$ mesons. The $D^* D \gamma$ coupling constants are found from the $D^* \to D \gamma$ decays. We find relatively large contribution for the $D^0 {\bar D}^0$ channel and much smaller contribution in the $D^+ D^-$ channel. In the second case we consider also the $D^{\pm}$ exchanges. We conclude that the bump at $M_{D^0 {\bar D}^0} = 3.8$ GeV observed by the Belle and BaBar Collaborations has rather continuum origin than it corresponds to the broad resonance $\chi_{c0}(3860)$. We discuss also production of the $\chi_{c2}(3930)$ resonance which is a candidate for the $\chi_{c2}(2P)$ state. This state can decay into both $D \bar{D}$ channels, however the branching fractions are not well known at present. From a comparison of our model results to the BaBar data we find $B(\chi_{c2}(3930) \to D \bar{D}) = 0.58 \pm 0.13$ using the two-photon width $\Gamma_{\gamma \gamma} = 0.544$ keV (obtained for the Buchm\"uller-Tye potential) evaluated within the light-front approach (NRQCD limit). Our finding of $\Gamma_{\gamma \gamma} \times B(\chi_{c2}(3930) \to D \bar{D}) = 0.32 \pm 0.07$ keV is close to the Belle and BaBar results. Realistic predictions of the differential distributions in several variables and integrated cross-sections are given for the Belle II kinematics.