  We calculate the polarization of prompt $\varUpsilon$($n$S) production in the
improved color evaporation model at leading order employing the
$k_T$-factorization approach. We present the polarization parameter
$\lambda_\vartheta$ of prompt $\varUpsilon$($n$S) as a function of transverse
momentum in $p+p$ and $p+\bar{p}$ collisions to compare with data in the
helicity, Collins-Soper and Gottfried-Jackson frames. We also present
calculations of the bottomonium production cross sections as a function of
transverse momentum and rapidity. This is the first $p_T$-dependent calculation
of bottomonium production and polarization in the improved color evaporation
model. We find agreement with both bottomonium cross sections and polarization
measurements.
