A consistent $\mathcal{O}(v^2)$ NRQCD description of decays and high-$P_T$ prompt production of charmonia

Abstract

We present a global determination of the six long-distance matrix elements (LDMEs) within non-relativistic QCD (NRQCD) appearing in the production of prompt $J/ψ$ up to $\mathcal{O}(v^2)$ using high-$P_T$ LHC data for direct and feed-down contributions from $χ_c$ and $ψ(2S)$. Using a leading-power fragmentation framework at NLO+NLL, we fit $ψ(2S)/J/ψ$ yield ratios from ATLAS and CMS and $ψ(2S)$ CMS polarization data at $\sqrt{s} = 13$ TeV, injecting one decay width per charmonium. The fit LDMEs provide excellent predictions of the CMS and ATLAS cross-section data up to $P_T=360$ GeV for the $J/ψ$, as well as the $J/ψ$ polarization data from CMS. The obtained excellent agreement with production and decay data demonstrates that $\mathcal{O}(v^2)$ NRQCD is sufficient to describe $J/ψ$, $ψ(2S)$, and $χ_c$ hadroproduction at large $P_T$.