The Roper and Radiative Decay of Pentaquarks

Identifying the Roper N(1440) and N(1710) as the pentaquark octet and anti-decuplet, respectively, we analyze their main decay modes in the diquark picture. The ratio of the partial decay widths is largely consistent with the nearly ideal mixing of the Jaffe-Wilczek diquark model, which then allows to predict the width of the radiative decay of N(1440), $\Gamma_{10}(N\to p\gamma)=1/4 \Gamma_{12}(N\to n\gamma)=0.25-0.31$ MeV. We then show that the three-body radiative decay of the pentaquark anti-decuplet is quite enhanced due to its mixing with the pentaquark octet. We find for the $J^P={1/2}^+$ pentaquark anti-decuplet $\Gamma(\Theta^+\to K^+ n \gamma)=0.034 \sim 0.041$ MeV. The diquark picture of the pentaquark predicts $\Gamma(\Theta^+\to K^+ n \gamma) =4 \Gamma(\Theta^+\to K^0 p \gamma)$. Finally we show that the difference in the Theta+ mass in the K0 p and K+ n decay channels may be accounted for by the missing photons in the radiative decay.