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.
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