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), $Γ_{10}(N\to pγ)=1/4 Γ_{12}(N\to nγ)=0.25-0.31$ 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 $Γ(Θ^+\to K^+ n γ)=0.034 \sim 0.041$ MeV. The diquark picture of the pentaquark predicts $Γ(Θ^+\to K^+ n γ) =4 Γ(Θ^+\to K^0 p γ)$. 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.