  Following the nonrelativistic QCD factorization scheme, by taking latest
available measurement on $\chi_b(3P)$ into consideration, we present an updated
study on the yield and polarization of $\Upsilon(1S,2S,3S)$ hadroproduction,
and the fractions of $\chi_b(mP)$ feed-down in $\Upsilon(nS)$ production at QCD
next-to-leading order. In the fitting, three schemes are applied with different
choice of $\chi_b(mP)$ feed-down ratios and NRQCD factorization scale. The
results can explain the measurements on yield very well as in our previous
work. The polarization puzzle to $\Upsilon(3S)$ is now solved by considering
the $\chi_b(3P)$ feed-down contributions. The ratio of
$\sigma[\chi_{b2}(1P)]/\sigma[\chi_{b1}(1P)]$ measurements from CMS can also be
reproduced in our prediction. Among the different schemes, the results show
little difference, but there are sizeable difference for the fitted
long-distance color-octet matrix elements. It may bring large uncertainty when
the values are applied in other experiments such as in $ee,~ep$ colliders.
