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We evaluate differential distributions for the four-body $p p \to n n \pi^+\pi^+$ reaction. The amplitude for the process is calculated in the Reggeapproach including many diagrams. We make predictions for possible futureexperiments at RHIC and LHC energies. Very large cross sections are found whichis partially due to interference of a few mechanisms. Presence of severalinterfering mechanisms precludes extraction of the elastic $\pi^+ \pi^+$scattering cross section. Absorption effects are estimated. Differentialdistributions in pseudorapidity, rapidity, invariant two-pion mass,transverse-momentum and energy distributions of neutrons are presented forproton-proton collisions at $\sqrt{s}$ = 500 GeV (RHIC) and $\sqrt{s}$ = 0.9,2.36 and 7 TeV (LHC). Cross sections with experimental cuts are presented.

Exclusive $pp \to nn \pi^{+}\pi^{+}$ reaction at LHC and RHIC