Exclusive production of two and four pions in proton-proton scattering

We consider exclusive $pp \to pp \pi^{+} \pi^{-}$ and $pp \to pp \pi^{+} \pi^{-}\pi^{+} \pi^{-}$ reactions 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. In the case of $pp \to pp \pi^{+} \pi^{-}$ process we consider both diffractive and photoproduction mechanisms and we include the non-resonant $\pi^{+}\pi^{-}$ continuum and the resonance $f_{0}(500)$, $f_{0}(980)$, $f_{2}(1270)$, $\rho(770)$ contributions. We discuss how two pomerons couple to tensor meson $f_{2}(1270)$ and the interference effects of resonance and dipion continuum. We find that the relative contribution of resonances $\rho(770)$, $f_2(1270)$ and dipion continuum strongly depends on the cut on proton transverse momenta. In the case of exclusive central $4 \pi$ production we include the contribution via the intermediate $\sigma\sigma$ and $\rho\rho$ states. For both processes the theoretical results have been compared with the experimental data and predictions for planned or being carried out experiments (e.g. STAR, ATLAS-ALFA) are presented.