Abstract
Following the nonrelativistic QCD factorization scheme, by taking the latest available measurements of χbJ(3P) into consideration, we present an updated study on the yield and polarization of ϒ(1S, 2S, 3S) hadroproduction, and the fractions of χbJ(mP) feed-down in ϒ(nS) production at QCD next-to-leading order. In the fitting, three schemes are applied with different choices of χbJ(mP) feed-down ratios and NRQCD factorization scale. The results can explain the measurements of yield very well. The polarization puzzle to ϒ(3S) is now solved by considering the χbJ(3P) feed-down contributions. The ratio of σ[χb2(1P)]/σ[χb1(1P)] measured by the CMS experiment can also be reproduced in our prediction. Among the different schemes, the results show little difference, but there are sizeable differences for the fitted long-distance color-octet matrix elements. This may bring large uncertainties when the values are applied in theoretical predictions for other experiments such as those at ee, ep colliders.
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