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We analize the reaction $pp\to \{pp\}_s\pi^0$ using one-loop diagrams with the subprocess $\pi^0 p \to \Delta p\pi^0$ \cite{uz2017}. The parameters for the coupling constants and vertex form factors which were used to explain the COSY data on the reaction $dp\to \{pp\}_s\pi N$ \cite{uzjhcw}, are applied here. The model explains the position of the peak observed at 0.6 GeV and zero diproton scattering angle \cite{komarov16}, but cannot describe the absolute value of the cross section and is in contradiction with the data on angular dependence. The helicity amplitudes formalism is developed in Ref. \cite{uz2017} for the partial wave analysis of this reaction including the state $J=4$. The developed model and helicity formalism can be applied for analysis of the new ANKE data on the resonance behaviour of this reaction at 1.5-2.5 GeV