Revision of absorption corrections for the $p p \to p p \pi^{+} \pi^{-}$ process

We include new additional absorption corrections into the Lebiedowicz-Szczurek (non-resonant) model for $p p \to p p \pi^+ \pi^-$ or $p \bar p \to p \bar p \pi^+ \pi^-$ processes. They are related to the $\pi N$ nonperturbative interaction in the final state of the reaction. The role of the absorption corrections is quantified for several differential distributions for $\sqrt{s}$ = 0.2, 1.96, 7, and 8 TeV. The new absorption corrections lead to further decrease of the cross section by about a factor of two. They change the shape of some distributions ($d \sigma / dt$, $d \sigma / dp_{t,p}$, $d \sigma/d \phi_{pp}$) but leave almost unchanged shape of other distributions ($d \sigma / dM_{\pi \pi}$, $d \sigma / dy_{\pi}$, $d \sigma /dp_{t,\pi}$, $d \sigma/ d \phi_{\pi \pi}$). The effect may have important impact on the interpretation of the recent STAR and CDF data as well as the forthcoming data of the ALICE, ATLAS + ALFA and CMS + TOTEM collaborations.