  We evaluate differential distributions for the four-body $p p \to p p K^{+}
K^{-}$ reaction at high energies which constitutes an irreducible background to
three-body processes $p p \to p p M$, where $M=\phi$, $f_{2}(1275)$,
$f_{0}(1500)$, $f_{2}'(1525)$, $\chi_{c0}$. We consider central diffractive
contribution mediated by Pomeron and Reggeon exchanges as well as completely
new mechanism of emission of kaons from the proton lines. We include absorption
effects due to proton-proton interaction and kaon-kaon rescattering. We compare
our results with measured cross sections for the CERN ISR experiment. We make
predictions for future experiments at RHIC, Tevatron and LHC. Differential
distributions in invariant two-kaon mass, kaon rapidities and transverse
momenta of kaons are presented. Two-dimensional distribution in $(y_{K^+},
y_{K^-})$ is particularly interesting. The higher the incident energy, the
higher preference for the same-hemisphere emission of kaons. We find that the
kaons from the new mechanism of emission directly from proton lines are
produced rather forward and backward but the corresponding cross section is
rather small. The processes considered here constitute a sizeable contribution
to the total proton-proton cross section as well as to kaon inclusive cross
section.
  We consider a measurement of exclusive production of scalar $\chi_{c0}$ meson
in the proton-proton collisions via $\chi_{c0} \to K^{+}K^{-}$ decay. The
corresponding amplitude for exclusive central diffractive $\chi_{c0}$ meson
production is calculated within the $k_{t}$-factorization approach. The
influence of kinematical cuts on the signal-to-background ratio is discussed.
