On relevance of triple gluon fusion in $J/ψ$ hadroproduction

TL;DR

The paper addresses the mismatch between data and leading-twist QCD in prompt $J/\psi$ hadroproduction by proposing a three-gluon (rescattering) mechanism analyzed within $k_T$-factorization. It develops analytic formulae for both uncorrelated and correlated triple-gluon contributions, and provides numerical estimates showing the uncorrelated term can yield about a 20–25% correction at moderate $p_T$, with a distinct polarization pattern that shifts toward longitudinal dominance at higher $p_T$. The study also discusses how the effect scales with nuclear size in $pA$ collisions, suggesting these measurements as a sensitive probe of the mechanism and of double-gluon densities at small $x$. Overall, the results indicate that multi-gluon rescattering is a significant, testable component that should be included in precision quarkonium phenomenology, especially when interpreting polarization and nuclear effects.

Abstract

A contribution to $J/ψ$ hadroproduction is analyzed in which the meson production is mediated by three-gluon partonic state, with two gluons coming from the target and one gluon from the projectile. This mechanism involves double gluon density in one of the protons, hence this contribution enters at a non-leading twist. It is, however, relevant due to an enhancement factor coming from large double gluon density at small~$x$. We calculate the three-gluon contribution to $J/ψ$ hadroproduction within perturbative QCD in the $k_T$-factorization framework. Results are obtained for differential $p_T$-dependent cross-sections for all $J/ψ$ polarizations and for the sum over the polarization components. The rescattering contribution is found to provide a significant correction to the standard leading twist cross-section at the energies of the Tevatron or the LHC at moderate $p_T$. We suggest $J/ψ$ production in proton-nucleus collision as a possible probe of the triple gluon mechanism.

Figures (9)

• Figure 1: a) The amplitude $\mathcal{M}$ of the $J/\psi$ hadroproduction in the triple gluon fusion mechanism; b) the dominant diagram in the square of the amplitude, $|\mathcal{M}|^2$.
• Figure 2: Topologies contributing to the rescattering correction in the $J/\psi$ cross-section : a) the topology with three two-gluon ladders (leading), b) the topology of two three-gluon BKP states (suppressed).
• Figure 3: The unintegrated gluon distribution.
• Figure 4: The correlated triple gluon contribution.
• Figure 5: Differential cross-sections for $J/\psi$ hadroproduction: a) $\left. \frac{d\sigma_{pp\rightarrow J/\psi X}}{dp_T}\right|_{|Y|<0.6} \times \mathrm{Br}(J/\psi \to \mu^+ \mu^-)$ at the Tevatron, $\sqrt{s} = 1.96$ TeV and b) $\left. \frac{d\sigma_{pp\rightarrow J/\psi X}}{dY\, dp_T}\right|_{|Y|<0.75} \times \mathrm{Br}(J/\psi \to \mu^+ \mu^-)$ at the LHC, $\sqrt{s} = 7$ TeV. The data-points shown: a) CDF CDFdata and b) ATLAS ATLASdata. The curves shown: bold continuous --- the triple gluon contribution computed in this paper, the dashed and dotted thin curves represent results of Ref. BK-NLOfit in the collinear approach: color singlet (LO and NLO) and combined color octet and color singlet results (see the legend in the plots).