  Central production of lepton-lepton pairs ($e^+e^-$ and $\mu^+\mu^-$) and
heavy quark composite states (charmonia and bottomonia) in diffractive proton
collisions (proton momenta transferred ${|\bf q_\perp}|\sim m/\ln s$) are
studied at ultrahigh energies ($\ln{s}>>1$), where
$\sigma_{tot}(pp^\pm)\sim\ln^N s$ with $1\la N\la 2$. The $pp^\pm$-rescattering
corrections, which are not small, are calculated in terms of the $K$-matrix
approach modified for ultrahigh energies. Two versions of hadron interactions
are considered in detail: the growth (i) $\sigma_{tot}(pp^\pm)\sim\ln^2 s$,
$\sigma_{inel}(pp^\pm)\sim\ln^2 s$ within the black disk mode and (ii)
$\sigma_{tot}(pp^\pm)\sim\ln^2 s$, $\sigma_{inel}(pp^\pm)\sim\ln s$ within the
resonant disk mode. The energy behavior of the diffractive production processes
differs strongly for these modes, thus giving a possibility to distinguish
between the versions of the ultrahigh energy interactions.

High Energy Physics - Phenomenology