On determining the cross section of the supposed pentaquark $ \Theta^{+}_{}$ in the reaction pp $ \rightarrow$ $ \Theta^{+}_{}$ $ \Sigma^{+}_{}$ $ \rightarrow$ pK0 $ \Sigma^{+}_{}$

Abstract

This paper addresses the problem of how to extract an upper limit on the cross section for $ \Theta^+$ production via the reaction $ pp\rightarrow\Theta^+\Sigma^+$ , where the $ \Theta^+$ is assumed to decay into the $ pK^0$ subsystem. Recent data of the COSY-TOF Collaboration, namely the angular distribution of protons in the $ \Sigma^+K^0$ helicity frame and the invariant mass spectrum of the $ pK^0$ system, were scrutinised with regard to a resonance by applying the profile likelihood method. It is found that the former distribution is best suited for setting an upper limit on the $ \Theta^+$ production, which varies between 90nb for an assumed $ \Theta^+$ mass of 1500MeV/c^2 and 56nb for 1540MeV/c^2.