${\bar D}D$ meson pair production in antiproton-nucleus collisions

We study the $\bar D D$ (${\bar D}^0 D^0$ and $D^-D^+$) charm meson pair production in antiproton (${\bar p}$) induced reactions on nuclei at beam energies ranging from threshold to several GeV. Our model is based on an effective Lagrangian approach that has only the baryon-meson degrees of freedom and involves the physical hadron masses. The reaction proceeds via the $t$-channel exchanges of $\Lambda_c^+$, $\Sigma_c^+$, and $\Sigma_c^{++}$ baryons in the initial collision of the antiproton with one of the protons of the target nucleus. The medium effects on the exchanged baryons are included by incorporating in the corresponding propagators, the effective charm baryon masses calculated within a quark-meson coupling (QMC) model. The wave functions of the bound proton have been determined within the QMC model as well as in a phenomenological model where they are obtained by solving the Dirac equation with appropriate scalar and vector potentials. The initial- and final-state distortion effects have been approximated by using an eikonal approximation-based procedure. Detailed numerical results are presented for total and double differential cross sections for the ${\bar D}^0 D^0$ and $D^-D^+$ production reactions on $^{16}$O and $^{90}$Zr targets. It is noticed that at ${\bar p}$ beam momenta of interest to the ${\bar P}ANDA$ experiment, medium effects lead to noticeable enhancements in the charm meson production cross sections.