The hadroproduction of mesons containing a b quark is analyzed in pert
urbative QCD. This analysis is performed to the fourth order in the co
upling constant alpha(s) for the production of two quark pairs and emp
loys the model of weak binding of quarks in the meson. The minimum tra
nsverse momentum above which the differential spectrum of mesons can b
e reliably described in the factorization model assuming that hard b-q
uark production is followed by fragmentation into mesons is determined
. At low transverse momenta of the product meson, there are significan
t contributions from nonfragmentation mechanisms that are described by
the full set of QCD diagrams of a given order in alpha(s). The nonfra
gmentation diagrams interfere destructively with the fragmentation dia
grams for z = 2E/root (s) over cap values that are close to unity.