  Inclusive cross sections for pion production in proton-proton collisions are
calculated for the first time based on unintegrated parton (gluon, quark,
antiquark) distributions (uPDF). We use Kwieci\'nski uPDF's and
phenomenological fragmentation functions from the literature. In addition to
the $gg \to g$ diagram used recently for applications at RHIC we include also
$g q \to q$ and $q g \to q$ diagrams. We find that the new contributions are
comparable to the purely gluonic one at midrapidities and dominate in the
fragmentation region. The new mechanisms are responsible for $\pi^+ - \pi^-$
asymmetry. We discuss how the asymmetry depends on $x_F$ and $p_t$. Inclusive
distributions in $x_F$ (or rapidity) and transverse momentum for partons and
pions are shown for illustration. In contrast to standard collinear approach in
our approach the range of applicability can be extended towards much lower
transverse momenta.
