pp → J/ψ plus Γ plus X as a clean probe to the quarkonium production mechanism

We report that, unlike most inclusive quarkonium-production processes, the production rate for pp -> J/psi + Gamma + X dominantly depends on two not well-known long-distance nonrelativistic QCD matrix elements, < O-8(J/psi)(S-3(1))> and < O-8(Gamma)(S-3(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 (c) over bar (8)(S-3(1)) -> J/psi and b (b) over bar (8)(S-3(1)) -> Gamma, respectively. With the integrated luminosity similar to 100 fb(-1) at the center-of-momentum energy root s = 14 TeV we expect that approximately 1900 pp -> J/psi + Gamma + 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/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.