  We evaluate differential distributions for the four-body $p p \to p p \pi^+
\pi^-$ reaction which constitutes a irreducible background to three-body
processes $p p \to p p M$, where $M$ are a broad resonances in the $\pi^+
\pi^-$ channel, e.g. $M=\sigma, \rho^{0}, f_{0}(980), f_{2}(1275),
f_{0}(1500)$. We include both double-diffractive contribution (both pomeron and
reggeon exchanges) as well as the pion-pion rescattering contribution. The
first process dominates at higher energies and small pion-pion invariant masses
while the second becomes important at lower energies and higher pion-pion
invariant masses. The amplitude(s) is(are) calculated in the Regge approach. We
compare our results with measured cross sections for the ISR experiments at
CERN. We make predictions for future experiments at PANDA, RHIC, Tevatron and
LHC energies. Differential distributions in effective two-pion mass, pion
rapidities and transverse momenta of pions are presented. The two-dimensional
distribution in $(y_{\pi^+}, y_{\pi^-})$ is particularly interesting. The
higher the incident energy, the higher preference for the same-hemisphere
emission of pions. The processes considered constitute a sizeable contribution
to the total nucleon-nucleon cross section as well as to pion inclusive cross
section.
