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

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 $D^{\ast }$ exchanges are considered. The results of the calculation depend on the parameter of the off-shell form-factor for the virtual $D^{\ast }$ mesons. The $D^{\ast }D\gamma$ coupling constants are found from the $D^{\ast }\to D\gamma$ 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 Buchmüller-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.

Comments: 14 pages, 5 figures, 3 tables