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Analysis of the Crystal Ball data on $K^-p\toπ^0Σ^0$ reaction with center-of-mass energies of $1536\sim 1676$ MeV

With an effective Lagrangian approach, we analyze the $K^-p\to π^0Σ^0$ reaction to study the $Λ$ hyperon resonances by fitting the Crystal Ball data on differential cross sections and $Σ^0$ polarization with the center-of-mass energies of $1536\sim 1676$ MeV. Besides well established PDG 4-star $Λ$ resonances around this energy range, the $Λ(1600){1\over 2}^+$ resonance, listed as a 3-star resonance in PDG, is found to be definitely needed. In addition, there is strong evidence for the existence of a new $Λ({3\over 2}^+)$ resonance around 1680 MeV.