  We compare the color-evaporation model (CEM) and nonrelativistic QCD (NRQCD)
factorization predictions for inclusive quarkonium production. Using the NRQCD
factorization formulas for quarkonium production and for perturbative QQ-bar
production, we deduce relationships that are implied by the CEM between the
nonperturbative NRQCD matrix elements that appear in the factorization formula
for quarkonium production. These relationships are at odds with the
phenomenological values of the matrix elements that have been extracted from
the Tevatron data for charmonium production at large transverse momentum. A
direct comparison of the CEM and NRQCD factorization predictions with the CDF
charmonium production data reveals that the CEM fits to the data are generally
unsatisfactory, while the NRQCD factorization fits are generally compatible
with the data. The inclusion of k_T smearing improves the CEM fits
substantially, but significant incompatibilities remain. The NRQCD
factorization fits to the chi_c data indicate that multiple gluon radiation is
an essential ingredient in obtaining the correct shape of the cross section as
a function of p_T.
