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

Employing the Bonn-Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction $p(3.5GeV)+pto pK^{+}Lambda$. This reaction might contain information about the kaonic cluster $ppK^-$ via its decay into $pLambda$. Due to interference effects in our coherent description of the data, a hypothetical $overline{K}NN$ (or, specifically $ppK^-$) cluster signal must not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectra like $pLambda$. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a $overline{K}NN$ cluster. At a confidence level of CL$_{s}$=95% such a cluster can not contribute more than 2-12% to the total cross section with a $pK^{+}Lambda$ final state, which translates 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.