Nucleon pole contribution in the $pp\to ppK^+K^-$ reaction below the $\phi$ meson threshold

Nucleon pole contribution in the $pp\to ppK^+K^-$ reaction below the threshold of the production of the $\phi$ meson is studied within the effective Lagrangian approach. It is assumed that the $K^- p$ final state originates from the decay of the hyperons $\Lambda(1115)$ and $\Lambda(1405)$. In addition to the $pp$ final state interaction (FSI) parametrized using the Jost function, we have also considered the $K^+K^-$ FSI with the techniques of the chiral unitary approach, where the scalar mesons $f_0(980)$ and $a_0(980)$ were dynamically generated. Hence, the contributions from scalar mesons $f_0(980)$ and $a_0(980)$ occur through the $K^+ K^-$ FSI. It is shown that the available experimental data are well reproduced, especially the total cross sections and the invariant mass distributions of $pp$ and $K^+K^-$. Furthermore, different forms of the couplings (pseudoscalar and pseudovector) for the $\pi NN$ interaction and different strengths for the proton-proton FSI are also investigated. It is found that the contributions from hyperon $\Lambda(1115)$ and $\Lambda(1405)$ are different between these two kinds of couplings. On the other hand, the effects of the proton-proton FSI can be adjusted by the cut off parameters used in the form factors.