Nucleon Resonances with Hidden Charm in $\gamma p $ reactions

The excitations of nucleon resonances with hidden charm, $N^*_{c\bar{c}}$, in the $\gamma p$ reactions are investigated by using the predictions from the available meson-baryons (MB) coupled-channel models. For the $\gamma\,p\rightarrow J/\psi\, p$ process, we first calculate the Pomeron-exchange amplitudes with the parameters determined from fitting the available total cross section data up to invariant mass $W=300$ GeV. We then add the resonant amplitudes to examine the effects of $N^*_{c\bar{c}}$ excitations on the cross sections of $\gamma\,p\rightarrow J/\psi\, p$ in the near threshold energy region. The $N^*_{c\bar{c}}\to MB$ transition matrix elements are determined from the partial decay widths predicted by the meson-baryons coupled-channel models. The $\gamma p \to N^*_{c\bar{c}}$ transition amplitudes are calculated from the Vector Meson Dominance (VMD) model. The total $\gamma p\rightarrow J/\psi\, p$ amplitudes then depend on an off-shell form factor, parameterized as $F_V(q^2)=\Lambda^4/(\Lambda^4 + (q^2 - m^2_V)^2)$ with $\Lambda=550$ MeV. We then demonstrate that the $N^*_{c\bar{c}}$ can be most easily identified in the differential cross sections at large angles of outgoing $J/\psi$ where the contribution from Pomeron-exchange becomes negligible. With the same VMD model and the same coupled-channel models of $N^*_{c\bar{c}}$, we also calculate the resonant amplitudes for the $\gamma\,p\rightarrow Vp\rightarrow N^*_{c\bar{c}} \rightarrow \bar{D}^0\Lambda_c^+ (\bar{D}^{*0}\Lambda_c^+)$ processes. By adding the non-resonant amplitudes due to the exchange of $\bar{D}^{*0}$ ($\bar{D}^{0})$, we then predict the cross sections of $\gamma\,p\rightarrow \bar{D}^0\Lambda_c^+(\bar{D}^{*0}\Lambda^+_c)$ for additional experimental tests of the available meson-baryon coupled-channel models of $N^*_{c\bar{c}}$.