A Phenomenological Lagrangian Approach to Two Kaon Photoproduction and Pentaquark Searches

We examine cross sections for the processes $\gamma N\to NK\bar{K}$ in the framework of a phenomenological Lagrangian. We include contributions from $\mathrm{\Lambda }$ and $\mathrm{\Sigma }$ resonances up to spin 3/2, as well as those from an exotic ${\mathrm{\Theta }}^{+}$. We allow the ${\mathrm{\Theta }}^{+}$ to have spin 1/2 or 3/2, with either positive or negative parity in each case. We also allow the state to be either isovector or isoscalar. We find that the scenario that most closely matches observations at Jefferson Laboratory requires a moderately large coupling of the ${\mathrm{\Theta }}^{+}$ to $N{K}^{\ast }$.