$\overline{p}p$ annihilation into $\overline{D}D$ meson pair within an effective Lagrangian model

We study the charmed meson pair (${\overline{D}}^0{D}^0$ and $D^{+}{D}^{-}$) production in $\overline{p}p$ annihilation within an effective Lagrangian model that has only the baryon-meson degrees of freedom and involves the physical hadron masses. The reaction amplitudes include terms corresponding to the $t$-channel ${\mathrm{\Lambda }}_c^{+}$, ${\mathrm{\Sigma }}_c^{+}$, and ${\mathrm{\Sigma }}_c^{++}$ baryon exchanges and the $s$-channel excitation, propagation and decay of the $\mathrm{\Psi }(3770)$ resonance into the charmed mesons. The initial- and final-state distortion effects have been accounted for by using a simple eikonal approximation-based procedure in the same way as was done in our previous study of the $\overline{p}p\to {\overline{\mathrm{\Lambda }}}_c^{-}{\mathrm{\Lambda }}_c^{+}$ reaction within a similar model. The ${\overline{D}}^0{D}^0$ production reaction is dominated by the ${\mathrm{\Lambda }}_c^{+}$ baryon exchange process and the corresponding total cross sections are predicted to be in the range of $0.18-0.7\mu \mathrm{b}$ for antiproton beam momenta varying between threshold and $20\mathrm{GeV}/\mathrm{c}$. The $\mathrm{\Psi }(3770)$ resonance contributions have a large influence on the differential cross sections of the $D^{-}{D}^{+}$ production reaction.

Figure 1

Graphical representation of the model used to describe the $\overline{p}+p\to {\overline{D}}^0+D^0$ (a) and $\overline{p}+p\to D^{-}+D^{+}$ (b) reactions via $t$-channel exchange of charmed baryons. In (a) ${\mathrm{\Lambda }}_c^{+}$ and ${\mathrm{\Sigma }}_c^{+}$ in the intermediate line represent the exchanges of ${\mathrm{\Lambda }}_c^{+}$ and ${\mathrm{\Sigma }}_c^{+}$ baryons, respectively while in (b) ${\mathrm{\Sigma }}_c^{++}$ represents the exchange of ${\mathrm{\Sigma }}_c^{++}$ baryon.

Figure 2

The Feynman diagram to describe the $\overline{p}+p\to \overline{D}+D$ reaction via $s$-channel excitation, propagation and decay of the $\mathrm{\Psi }(3770)$ resonance.

Figure 3

The distortion factor ${\mathrm{\Omega }}_{\overline{p}p}$ [defined by Eq. (11)] as a function of the antiproton beam momentum. The values of the parameters $\mu$, $V_0$ and $b$ were taken to be 0.3369 GeV, 0.8965 GeV and $0.3270{\mathrm{GeV}}^{-1}$, respectively, which are the same as those used in Ref. [29].

Figure 4

Total cross section for the $\overline{p}p\to \mathrm{\Psi }(3770)\to {\overline{D}}^0{D}^0$ reaction as a function of the antiproton beam momentum. The solid line represents the cross sections calculated within the resonance production and decay model [Eq. (9)], while the dashed line shows the effective Lagrangian model cross sections [obtained with the amplitude given by Eq. (7)].

Figure 5

(a) Total cross section for the $\overline{p}p\to {\overline{D}}^0{D}^0$ reaction as a function of the antiproton beam momentum. The solid and dashed lines represent the cross sections obtained by the coherent sum of the $t$-channel baryonic exchange and the $s$-channel $\mathrm{\Psi }(3770)$ resonance excitation amplitudes, and by including the $t$-channel baryon exchange contributions only in the amplitude, respectively. (b) The same for the $\overline{p}p\to D^{-}{D}^{+}$ reaction as a function of the antiproton beam momentum. The full and dashed lines have the same meaning as in (a).

Figure 6

(a) Differential cross section for the $\overline{p}p\to {\overline{D}}^0{D}^0$ reaction at the antiproton beam momentum of $6.57\mathrm{GeV}/\mathrm{c}$. The solid and dashed lines have the same meanings as those in Fig. 5. (b) The same as in (a) but for the $\overline{p}p\to D^{-}{D}^{+}$ reaction.

Figure 7

Total cross section for the $\overline{p}p\to {\overline{D}}^0{D}^0$ reaction as a function of the antiproton beam momentum. The contributions of $t$-channel ${\mathrm{\Lambda }}_c^{+}$ and ${\mathrm{\Sigma }}_c^{+}$ baryon exchange processes are shown by dashed and dashed-dotted lines, respectively, while the dotted line represents the cross sections of the $s$-channel $\mathrm{\Psi }(3770)$ resonance excitation. The cross sections corresponding to the coherent sum of these amplitudes are shown by the full curve.

Figure 8

Total cross section for the $\overline{p}p\to D^{-}{D}^{+}$ reaction as a function of the antiproton beam momentum. The contributions of $t$-channel ${\mathrm{\Sigma }}_c^{++}$ baryon exchange and $s$-channel $\mathrm{\Psi }(3770)$ resonance excitation are shown by dashed and dash-dotted lines respectively. The cross sections corresponding to the coherent sum of these terms in the total amplitudes are shown by the full curve.

Figure 9

Differential cross section for the $\overline{p}p\to {\overline{D}}^0{D}^0$ reaction at the antiproton beam momenta of 8, 10, 12 and $16\mathrm{GeV}/\mathrm{c}$ as indicated in the figure. The solid lines show the cross sections where the amplitudes of the $t$-channel ${\mathrm{\Lambda }}_c^{+}$, and ${\mathrm{\Sigma }}_c^{+}$ baryon exchange and $s$-channel $\mathrm{\Psi }(3770)$ resonance terms are coherently added. The dashed lines show the cross sections where the amplitudes include the contributions of the ${\lambda }_c^{+}$-exchange term only.

Figure 10

Differential cross section for the $\overline{p}p\to D^{-}{D}^{+}$ reaction for antiproton beam momenta of 8, 10, 12 and $16\mathrm{GeV}/\mathrm{c}$. The dashed lines show the contributions of the ${\mathrm{\Sigma }}_c^{++}$ baryon exchange terms only while the solid line represents the cross sections where the amplitudes of ${\mathrm{\Sigma }}_c^{++}$ baryon exchange and $\mathrm{\Psi }(3770)$ resonance terms are coherently added.