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$Υ(nS)$ and $χ_b(nP)$ production at hadron colliders in nonrelativistic QCD

$Υ(nS)$ and $χ_b(nP)$ (n=1,2,3) production at the LHC is studied at next-to-leading order in $α_s$ in nonrelativistic QCD. Feeddown contributions from higher $χ_b$ and $Υ$ states are all considered for lower $Υ$ cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the $Υ(nS)$ polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the $Υ(3S)$ polarization puzzle can be understood by a large feeddown contribution from $χ_b(3P)$ states. Our results may provide a good description for both cross sections and polarizations of prompt $Υ(nS)$ and $χ_b(nP)$ production at the LHC.