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Employing the Bonn-Gatchina partial wave analysis framework (PWA), we haveanalyzed HADES data of the reaction $p(3.5GeV)+p\to pK^{+}\Lambda$. Thisreaction might contain information about the kaonic cluster "$ppK^-$" via itsdecay into $p\Lambda$. Due to interference effects in our coherent descriptionof the data, a hypothetical $\overline{K}NN$ (or, specifically "$ppK^-$")cluster signal must not necessarily show up as a pronounced feature (e.g. apeak) in an invariant mass spectra like $p\Lambda$. Our PWA analysis includes avariety of resonant and non-resonant intermediate states and delivers a gooddescription of our data (various angular distributions and two-hadron invariantmass spectra) without a contribution of a $\overline{K}NN$ cluster. At aconfidence level of CL$_{s}$=95\% such a cluster can not contribute more than2-12\% to the total cross section with a $pK^{+}\Lambda$ final state, whichtranslates into a production cross-section between 0.7 $\mu b$ and 4.2 $\mu b$,respectively. The range of the upper limit depends on the assumed cluster mass,width and production process.

Partial Wave Analysis of the Reaction $p(3.5 GeV)+p \to pK^+\Lambda$ to Search for the "$ppK^-$" Bound State