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.
Download