An Updated Study for $Υ$ Production and Polarization at the Tevatron and LHC

Following the nonrelativistic QCD factorization scheme, by taking latest available measurement on $χ_b(3P)$ into consideration, we present an updated study on the yield and polarization of $Υ(1S,2S,3S)$ hadroproduction, and the fractions of $χ_b(mP)$ feed-down in $Υ(nS)$ production at QCD next-to-leading order. In the fitting, three schemes are applied with different choice of $χ_b(mP)$ 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 $Υ(3S)$ is now solved by considering the $χ_b(3P)$ feed-down contributions. The ratio of $σ[χ_{b2}(1P)]/σ[χ_{b1}(1P)]$ 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.

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