${\rm Y}(1S)$ prompt production at the Tevatron and LHC in nonrelativistic QCD

Abstract

With nonrelativistic QCD factorization, we calculate the ${\rm Y}(1S)$ prompt production at hadron colliders at next-to-leading order in ${\alpha }_s$. In addition to the color-singlet contribution, color-octet channels (especially the P-wave channel) up to $O(v^4)$ are all considered. Aside from direct production, the feed-down contributions from higher excited S-wave and P-wave $b\bar{b}$ states to ${\rm Y}(1S)$ production are also included. We use the potential model estimates as input for color-singlet long-distance matrix elements (LDMEs). While for color-octet contributions, we find they can be approximately described by three LDMEs: $\mo{}{3}{S}{1}{8}$, $\mo{}{1}{S}{0}{8}$ and $\mo{}{3}{P}{0}{8}$. By fitting the Tevatron data we can determine some linear combinations of these LDMEs, and then use them to predict ${\rm Y}(1S)$ production at the LHC. Our predictions are consistent with the new experimental data of CMS and LHCb.

Version published in PRD, references added, 15 pages, 3 figures

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