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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mo>+</mml:mo><mml:mi>Υ</mml:mi><mml:mo>+</mml:mo><mml:mi>X</mml:mi></mml:math>as a clean probe to the quarkonium production mechanism
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 $b{\overline{b}}_{8}(^{3}S_{1})\ensuremath{\rightarrow}\ensuremath{\Upsilon}$, …