$J/\psi N$ photoproduction on deuterium as a test for exotic baryons

We extend a previous study of photoproduction of exotic baryon resonances to the reaction $\gamma + d \to J/\psi + n + p$, which permits simultaneous investigation of the reactions $\gamma + p \to P_c^+ \to J/\psi~p$ \hbox{($n$ spectator)} and $\gamma + n \to P_c^0 \to J/\psi~n$ \hbox{($p$ spectator).} Here $P_c^+$ is an exotic baryon with quark content $c \bar c uud$, and $P_c^0$ is its hypothetical isospin partner with quark content $c \bar c ddu$. We find: \hbox{(1) The} cross section for $J/\psi~n$ photoproduction should be equal to that for $J/\psi~p$ photoproduction if these processes are dominated by the photon coupling to a $c\bar c$ pair. In that case the two processes are equal by isospin reflection. (2) If a $P_c^+$ candidate is a genuine $c \bar c u u d$ resonance, its isospin partner $P_c^0 = c \bar c d d u$ should have the same mass (again by isospin reflection). (3) In the absence of Fermi motion, the cross section for photoproduction of $P_c$ off a deuteron should be nearly the sum of two equal cross sections: $\sigma(\gamma p \to P_c^+)$ (spectator $n$) and $\sigma(\gamma n \to P_c^0)$ (spectator $p$). (4) The effects of Fermi motion are significant. They include smearing, form-factor suppression and offshellness. The upshot is that the resonance is significantly wider and the peak cross section off a deuteron is expected to be considerably less than twice that in $\gamma p$.