Photo-production of the pentaquark $\Theta^{+}$ with positive and negative parities

We investigate the production of the pentaquark $\Theta^+$ baryon via the $\gamma n\to K^-\Theta^+$ and $\gamma p\to \bar{K}^0 \Theta^+$ processes, focusing on the parity of the $\Theta^+$. Using the effective Lagrangians, we calculate the total and differential cross sections with the spin of the $\Theta^+$ presumed to be 1/2. We employ the coupling constant of the $KN\Theta$ vertex determined by assuming its mass and the decay width to be $1540 {\rm MeV}$ and $15 {\rm MeV}$. That of the $K^*N\Theta$ is taken to be about a half of the $KN\Theta$ coupling constant. We estimate the cutoff parameter by reproducing the total cross section of the $\gamma p \to K^+ \Lambda$ reaction. It turns out that the total cross section for the $\gamma n\to K^- \Theta^+$ process is about four times larger than that of the $\gamma p\to\bar{K}^0\Theta^+$. We also find that the cross sections for the production of the positive-parity $\Theta$ are about ten times as large as those for the negative-parity ones.