PromptΥ(nS)production at the LHC in the Regge limit of QCD

Abstract

We study prompt $\ensuremath{\Upsilon}(nS)$ hadroproduction ($n=1$, 2, 3) invoking the hypothesis of gluon Reggeization in $t$-channel exchanges at high energy and the factorization formalism of nonrelativistic quantum chromodynamics at leading order in the strong-coupling constant ${\ensuremath{\alpha}}_{s}$ and the relative velocity $v$ of the bound quarks. The transverse-momentum distributions of prompt $\ensuremath{\Upsilon}(nS)$-meson production measured by the ATLAS Collaboration at the CERN LHC are fitted to obtain the color-octet nonperturbative long-distance matrix elements, which are used to predict prompt $\ensuremath{\Upsilon}(nS)$ production spectra measured by the CMS and LHCb Collaborations. At the numerical calculation, we adopt the Kimber-Martin-Ryskin prescription to derive unintegrated gluon distribution function of the proton from its collinear counterpart, for which we use the Martin-Roberts-Stirling-Thorne set. We find good agreement with measurements by the ATLAS, CMS, and LHCb Collaborations at the LHC at the hadronic c.m. energy $\sqrt{S}=7\text{ }\text{ }\mathrm{TeV}$ as well as with measurements by the CDF Collaboration at the Fermilab Tevatron.