Exclusive diffractive production of hadrons in $pp$ collisions

We discuss central exclusive diffractive dihadron production in proton-proton collisions at high energies. The calculation is based on a tensor pomeron model and the amplitudes for the processes are formulated in an effective field-theoretic approach. We include a purely diffractive dipion continuum, and the scalar and tensor resonances decaying into the $\pi^{+} \pi^{-}$ pairs as well as the photoproduction contributions ($\rho^{0}$, Drell-S\"oding). We discuss how two pomerons couple to tensor meson $f_{2}(1270)$ and the interference effects of the scalar and tensor resonances and the dipion continuum. The theoretical results are compared with existing CDF and CMS experimental data. We discuss also the Drell-Hiida-Deck type mechanism with centrally produced $\rho^{0}$ meson associated with a very forward/backward $\pi N$ system. For the $pp \to pp \pi^{+} \pi^{-} \pi^{+} \pi^{-}$ reaction we consider both the $\sigma \sigma$ and $\rho \rho$ contributions as well as the triple Regge exchange mechanism. Predictions for planned or being carried out experiments (STAR, ALICE, ATLAS, CMS) are presented. We show the influence of the experimental cuts on the integrated cross section and on various differential distributions for outgoing particles.