  We discuss central exclusive diffractive production of light mesons in the
reactions $pp \to pp\pi^{+}\pi^{-}$ and $pp \to ppK^{+}K^{-}$. The calculation
is based on a tensor-pomeron approach. We include a purely diffractive dipion
continuum, and the scalar $f_{0}(980)$, $f_{0}(1500)$, $f_{0}(1710)$ and tensor
$f_{2}(1270)$, $f'_{2}(1525)$ resonances decaying into pseudoscalar meson
pairs. We include also photoproduction mechanisms for the nonresonant
(Drell-S\"oding) and the $\phi(1020)$ resonance contributions. The theoretical
results are compared with existing CDF experimental data and predictions for
being carried out LHC experiments are presented. The distributions in dimeson
invariant mass and in a special "glueball filter variable" including the
interference effects of resonance and dimeson continuum are presented.
