Study on the inclusive hadroproduction of Υ plus γ at next-to-leading order

In this paper we investigate the inclusive associated production of Upsilon + gamma at hadron colliders. We calculate the color-singlet subprocesses and all three color-octet subprocesses 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 giving the unphysical results on the yield and the polarization for this process. The yield could be enhanced by several times or even two orders of magnitude compared to the color-singlet contribution and the polarization changes from longitudinal to slightly transverse or even mainly transverse in the large p(t) region. The estimated 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).