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We report a theoretical study of the $pp\to p K^+\Lambda(1405)$ reaction,which was recently investigated at COSY-J\"{u}lich by using a 3.65 GeV/ccirculating proton beam incident on an internal hydrogen target. The reactionis driven by single kaon exchange, single pion exchange, and single rhoexchange terms which have very different shapes due to the two pole structureof the $\Lambda(1405)$ and the presence of background terms. The shape for thesum of the three contributions, as well as the total cross section, areconsistent with present data within experimental and theoretical uncertainties,using reasonable form factors for the meson-baryon vertices.

The role of the $\Lambda(1405)$ in the $pp\to p K^+\Lambda(1405)$ reaction