Exclusive diffractive production of $\pi^+ \pi^-$ pairs within tensor pomeron approach

We discuss exclusive central diffractive production of $\pi^{+} \pi^{-}$ in proton-(anti)proton collisions at high energies. Based on a tensor pomeron model we present results of the purely diffractive dipion continuum, the scalar $f_{0}(500)$, $f_{0}(980)$ and tensor $f_{2}(1270)$ resonances decaying into the $\pi^{+} \pi^{-}$ pairs as well as the photoproduction mechanism ($\rho^{0}$, Drell-S\"oding). We discuss how two pomerons couple to the tensor meson $f_{2}(1270)$ and the interference effects of resonance and dipion continuum contributions. The theoretical results are compared with existing STAR, CDF, and CMS experimental data. Predictions for planned or being carried out experiments (ALICE, ATLAS) are presented. We find that the relative contribution of resonant $f_2(1270)$ and dipion continuum strongly depend on the cut on proton transverse momenta (or four-momentum transfer squared $t_{1,2}$) which may explain some controversial observations made by different ISR experiments in the past. The cuts may play then the role of a $\pi \pi$ resonance filter.