$\Upsilon(1S)$ prompt production at the Tevatron and LHC in nonrelativistic QCD

TL;DR

This paper calculates the prompt production of $1S)$ at hadron colliders using nonrelativistic QCD, including color-singlet and octet channels, and fits data to predict outcomes at the LHC.

Contribution

It provides a comprehensive NLO calculation of $1S)$ production including feed-down effects and fits LDMEs to experimental data for accurate predictions.

Findings

Color-octet contributions can be described by three key LDMEs.

Fitted LDMEs from Tevatron data predict LHC $1S)$ production.

Predictions agree with CMS and LHCb measurements.

Abstract

With nonrelativistic QCD factorization, we calculate the $\Upsilon(1S)$ 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 $\Upsilon(1S)$ 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 $\Upsilon(1S)$ production at the LHC. Our predictions are consistent with the new experimental data of CMS and LHCb.