Associate K^0 production in p+p collisions at 3.5 GeV: The role of Delta(1232)++

An exclusive analysis of the 4-body final states $mathrm{Lambda + p + pi^{+} + K^{0}}$ and $mathrm{Sigma^{0} + p + pi^{+} + K^{0}}$ measured with HADES for p+p collisions at a beam kinetic energy of 3.5 GeV is presented. The analysis uses various phase space variables, such as missing mass and invariant mass distributions, in the four particle event selection (p, $pi^+$, $pi^+$, $pi^-$) to find cross sections of the different production channels, contributions of the intermediate resonances $mathrm{Delta^{++}}$ and $mathrm{Sigma(1385)^{+}}$ and corresponding angular distributions. A dominant resonant production is seen, where the reaction $mathrm{Lambda + Delta^{++} + K^{0}}$ has an about ten times higher cross section ($mathrm{29.45pm0.08^{+1.67}_{-1.46}pm2.06,mu b}$) than the analogous non-resonant reaction ($mathrm{2.57pm0.02^{+0.21}_{-1.98}pm0.18,mu b}$). A similar result is obtained in the corresponding $Sigma^{0}$ channels with $mathrm{9.26pm0.05^{+1.41}_{-0.31}pm0.65, mu b}$ in the resonant and $mathrm{1.35pm0.02^{+0.10}_{-1.35}pm0.09,mu b}$ in the non-resonant reactions.