The Roper and Radiative Decay of Pentaquarks

Abstract

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.

Comments: 10pages, 10 figures; Minor typos corrected: V3 added discussions on mass difference in theta+ in K0 p and K+ n: V4. Erros in numerical analysis corrected