Effects of a $N_{c\overline{c}}^{*}$ resonance with hidden charm in the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction near threshold

We study the effect of a hidden charm nuclear excited state $N_{c\overline{c}}^{*}$ in the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction near threshold using an effective Lagrangian approach. We calculate the background contribution of the $t$ and $u$ channels by the $D^{*0}$ vector meson exchange and ${\mathrm{\Sigma }}_c^{++}$ intermediate state, respectively. We show that the consideration of a $N_{c\overline{c}}^{*}$ resonance provides an enhancement of the total cross section close to the reaction threshold. We also evaluate the differential cross section for different energies and we study the angle dependence. It is expected that our model calculations will be tested in future experiments.

Figure 1

Diagrams considered in the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction. The contributions from $t$ channel $D^{*0}$ exchange (a), $u$ channel ${\mathrm{\Sigma }}_c^{++}$ exchange (b), and $s$ channel $N_{c\overline{c}}^{*}$ resonance (c) are considered.

Figure 2

Comparison of the total cross section of the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction: (solid line) total cross section including $N_{c\overline{c}}^{*}\left(4261\right)$, (dotted line) cross section of the background ($t$ and $u$ channels), and (dashed line) cross section for the $s$ channel $\left[N_{c\overline{c}}^{*}\left(4261\right)\right]$ only.

Figure 3

Differential cross section of the ${\pi }^{-}p\to D^{-}{\mathrm{\Sigma }}_c^{+}$ reaction at different energies in the center of mass frame: $W=4.35$ GeV (solid line), $W=4.45$ GeV (dashed line), and $W=4.55$ GeV (dotted line).