Pp→J/ψ+Υ+Xas a clean probe to the quarkonium production mechanism

Abstract

We report that, unlike most inclusive quarkonium-production processes, the production rate for $pp\ensuremath{\rightarrow}J/\ensuremath{\psi}+\ensuremath{\Upsilon}+X$ dominantly depends on two not well-known long-distance nonrelativistic QCD matrix elements, $⟨{O}_{8}^{J/\ensuremath{\psi}}(^{3}S_{1})⟩$ and $⟨{O}_{8}^{\ensuremath{\Upsilon}}(^{3}S_{1})⟩$ at leading order in the strong coupling constant, which account for the transition probabilities of the color-octet spin-triplet heavy-quark-antiquark pairs $c{\overline{c}}_{8}(^{3}S_{1})\ensuremath{\rightarrow}J/\ensuremath{\psi}$ and $b{\overline{b}}_{8}(^{3}S_{1})\ensuremath{\rightarrow}\ensuremath{\Upsilon}$, respectively. With the integrated luminosity $\ensuremath{\sim}100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at the center-of-momentum energy $\sqrt{s}=14\text{ }\text{ }\mathrm{TeV}$ we expect that approximately 1900 $pp\ensuremath{\rightarrow}J/\ensuremath{\psi}+\ensuremath{\Upsilon}+X$ events can be observed at the CERN Large Hadron Collider by tagging muon pairs, which are enough to probe to the color-octet mechanism. The forthcoming measurement may provide a useful constraint to resolve the decade-old puzzle for the polarization of prompt $J/\ensuremath{\psi}$ at the Fermilab Tevatron. If corresponding measured rate is significantly less than the prediction, it may imply that the current values for the color-octet matrix elements are overestimated.