How well does NRQCD describe quarkonium production?

Abstract

The question how well nonrelativistic QCD (NRQCD) factorization can describe quarkonium production has been subject to debate since its invention. We review our recent reanalysis of a classic next-to-leading order color octet (CO) long distance matrix element (LDME) fit to large transverse momentum $p_T$ $J/ψ$ and $η_c$ LHC production data. Our analysis differs from previous analyses of this kind not only by implementing for the first time a systematic treatment of scale uncertainties, but also by scrutinizing a much broader range of observables. Surprisingly, $J/ψ$ hadroproduction is well described up to the highest measured values of $p_T$. Potential NRQCD based relations nontrivially lead to a perfect description of $Υ(nS)$ production data. Furthermore, $J/ψ$ production in $γp$ and $γγ$ collisions is, contrary to prevailing conceptions, reproduced down to $p_T=1$ GeV, as long as the region of large inelasticity $z$ is excluded. The overall picture is much rosier than usually perceived, the more so as the remaining discrepancies appear in phase space regions where solutions via varying kinds of resummations have been proposed.

Figures (2)

• Figure 1: The fit to prompt $J/\psi$ production at CMS CMS:2015lbl and $\eta_c$ production at LHCb LHCb:2014oiiLHCb:2024ydi. The total cross section is broken down into feeddown contributions and the direct contributions of the individual Fock states. The orange bands describe the uncertainties from the fit correlations, the orange band additionally the effect of scale variations as described in section \ref{['sec:fit']}.
• Figure 2: Theory predictions for the $J/\psi$ polarization parameter $\lambda_{\theta}$ in the helicity frame compared to CMS CMS:2013gbzCMS:2024igk (a) and LHCb LHCb:2013izl (b) data, for $J/\psi$ hadroproduction measured by ATLAS ATLAS:2023qnh (c) and LHCb LHCb:2015foc (d), for $\Upsilon(3S)$ATLAS:2012lmu (e) and single-parton scattering (SPS) $J/\psi+Z$ATLAS:2014ofp (f) production measured by ATLAS, for LEP DELPHI two photon collision data DELPHI:2003hen (g), and for HERA H1 H1:2010udv and ZEUS ZEUS:2012qog photoproduction data (h--l). Panels (g) to (l) show the sum of non-, single- (and double-) resolved photon contributions, which are not broken down here, to avoid clutter. In all panels, the total cross sections are broken down into feeddown contributions and the direct contributions of the individual Fock states. The orange bands describe the uncertainties from the fit correlations, the yellow band additionally the effect of scale variations as described in section \ref{['sec:fit']}.