Exclusive $\pi^+\pi^-$ Production at the LHC with Forward Proton Tagging

A process of Central Exclusive $\pi^+\pi^-$ production in proton-proton collisions and its theoretical description is presented. A possibility of its measurement, during the special low luminosity LHC runs, with the help of the ATLAS central detector for measuring pions and the ALFA stations for tagging the scattered protons is studied. A visible cross section is estimated to be 21 $\mu$b for $\sqrt{s}=7$ TeV, which gives over 2000 events for 100 $\mu$b$^{-1}$ of integrated luminosity. Differential distributions in pion pseudorapidities, pion and proton transverse momenta as well as $\pi^+\pi^-$ invariant mass are shown and discussed.