$pp \to pK^{+}\Lambda$ reaction in an effective Lagrangian model

We investigate the $pp \to pK^{+}\Lambda$ reaction within an effective Lagrangian model where the contributions to the amplitudes are taken into account within the tree level. The initial interaction between the two nucleons is modeled by the exchange of $\pi$, $\rho$, $\omega$ and $\sigma$ mesons and the $\Lambda K^{+}$ production proceeds via the excitation of the $N^*$(1650), $N^*$(1710), $N^*$(1720) baryonic resonances. The parameters of the model at the nucleon-nucleon-meson vertices are determined by fitting the elastic nucleon-nucleon scattering with an effective interaction based on the exchange of these four mesons, while those at the resonance vertices are calculated from the known decay widths of the resonances as well as the vector meson dominance model. Available experimental data is described well by this approach. The one-pion-exchange diagram dominates the production process at both higher and lower beam energies. The $\rho$ and $\omega$ meson exchanges make negligible contributions. However, the $\sigma$-exchange processes contribute substantially to the total cross sections at lower beam energies. The excitation of the $N^*$(1710) and $N^*$(1650) resonances dominate this reaction at beam momenta above and below 3 GeV/c respectively. The interference among the amplitudes of various resonance excitation processes is significant. For beam energies very close to the $K^{+}$ production threshold the hyperon-proton final state interaction effects are quite important. The data is selective about the model used to describe the low energy scattering of the two final state baryons.