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The continuum mechanism with the t/u-channel $D^∗$ exchanges are considered [1]. The results 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 smaller contribution in the $D^+ D^−$ channel. In the second case we consider the $D^±$ exchanges. The bump at $M_{D^0 {\bar D}^0}$=3.8 GeV observed by the Belle and BaBar has continuum origin than it corresponds to the broad resonance $\chi_{c0}(3860)$. We discuss production of the $\chi_{c2}(3930)$ resonance which is a candidate for the $\chi_{c2}(2P)$ state. This state decays into both $D \bar D$ channels, however the branching fractions are not well known. From a comparison of our model results to the BaBar data we find $B(\chi_{c2}(3930)\to D\bar D)$=0.58±0.13 using $\Gamma_{\gamma\gamma}$=0.544 keV (Buchmuller-Tye potential) evaluated within the light-front approach (NRQCD limit). Realistic predictions of the differential distributions in several variables are given for the Belle II kinematics.In summary, we explain the invariant mass distributions of $D\bar D$ mesons as a combination of continuum and $\chi_c(2P)$ resonances.
[1] I. Babiarz, P. Lebiedowicz, W. Schaefer and A. Szczurek,
arXiv2511.16862, in print in Phys.Lett.B.
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