# The complete study on the inclusive production of {\Upsilon} + {\gamma} at the LHC

## TL;DR

This study comprehensively analyzes the production of Upsilon plus a photon at the LHC, including next-to-leading order calculations of various subprocesses, revealing challenges in experimental measurement and potential for future collider studies.

## Contribution

It provides the first detailed NLO calculation of all subprocesses for Upsilon + gamma production, highlighting issues with certain LDME sets and implications for collider experiments.

## Key findings

- Yield is significantly enhanced compared to color-singlet predictions.
- Polarization shifts from longitudinal to transverse at high transverse momentum.
- Some LDME sets produce unphysical results for yield and polarization.

## Abstract

In this paper we investigate the inclusive associated production of {\Upsilon} + {\gamma} at the hadron collider. We calculate the color-singlet sub-processes and all three color-octet sub-processes at the next-to-leading order. Seven sets of long distance matrix elements(LDMEs), which are extracted from the studies on the prompt production of {\Upsilon} at hadron colliders, are used to give the numerical results and we find that there are three sets of LDMEs give the unphysical results on the yield and the polarization for this process. The yield is enhanced by several or two orders times comparing to that of color-singlet process and the polarization changes from longitudinal to slightly transverse or even mainly transverse in the large pt region. The estimation results indicate that to study the process at the large hadron collider (LHC) is difficult and it may be well investigated at the future Super Proton-Proton Collider(SPPC).