Fragmentation contributions to hadroproduction of prompt $J/ψ$, $χ_{cJ}$, and $ψ(2S)$ states

TL;DR

This work refines NRQCD-based predictions for hadroproduction of charmonium states by computing leading-power fragmentation corrections and resumming leading logarithms in $p_T^2/m_c^2$. By combining LP fragmentation with NLO short-distance coefficients and fitting to Tevatron/LHC data, the authors extract NRQCD LDMEs for $J/\psi$, $\psi(2S)$, and $\chi_{cJ}$, then use these to predict cross sections and polarizations, including feeddown effects. The results show good agreement with many cross-section and polarization measurements, though some tensions remain (notably the CDF Run II $J/\psi$ polarization) and fundamental NRQCD issues with photoproduction and $\eta_c$ hadroproduction persist. The study highlights substantial LP corrections at high $p_T$ and emphasizes the need for complete higher-order LP calculations and more precise data to fully validate NRQCD factorization in quarkonium production.

Abstract

We compute fragmentation corrections to hadroproduction of the quarkonium states $J/ψ$, $χ_{cJ}$, and $ψ(2S)$ at leading power in $m_c^2/p_T^2$, where $m_c$ is the charm-quark mass and $p_T$ is the quarkonium transverse momentum. The computation is carried out in the framework of nonrelativistic QCD. We include corrections to the parton-production cross sections through next-to-leading order in the strong coupling $α_s$ and corrections to the fragmentation functions through second order in $α_s$. We also sum leading logarithms of $p_T^2/m_c^2$ to all orders in perturbation theory. We find that, when we combine these leading-power fragmentation corrections with fixed-order calculations through next-to-leading order in $α_s$, we are able to obtain good fits for $p_T\geq 10$ GeV to hadroproduction cross sections that were measured at the Tevatron and the LHC. Using values for the nonperturbative long-distance matrix elements that we extract from the cross-section fits, we make predictions for the polarizations of the quarkonium states. We obtain good agreement with measurements of the polarizations, with the exception of the CDF Run II measurement of the prompt $J/ψ$ polarization, for which the agreement is only fair. In the predictions for the prompt-$J/ψ$ cross sections and polarizations, we take into account feeddown from the $χ_{cJ}$ and $ψ(2S)$ states.

Figures (21)

• Figure 1: The ratio $(d\sigma^{\textrm{LP}}_{\rm NLO}/dp_T) / (d\sigma_{\rm NLO}/dp_T)$ for the ${}^1S_0^{[8]}$, ${}^3P_J^{[8]}$, and ${}^3S_1^{[8]}$ channels in the process $p p \to H + X$ at $\sqrt{s}=7$ TeV and $|y|<1.2$.
• Figure 2: The ratio $(d\sigma^{\textrm{LP}}_{\rm NLO}/dp_T) / (d\sigma_{\rm NLO}/dp_T)$ for the polarized ${}^3P_J^{[8]}$ and ${}^3S_1^{[8]}$ channels with longitudinal final states in the process $p p \to H + X$ at $\sqrt{s}=7$ TeV and $|y|<1.2$.
• Figure 3: The ratio $(d\sigma^{\textrm{LP}}_{\rm NLO}/dp_T) / (d\sigma_{\rm NLO}/dp_T)$ for the ${}^3P_1^{[1]}$ and ${}^3P_2^{[1]}$ channels in the process $p p \to H + X$ at $\sqrt{s}=7$ TeV and $|y|<1.2$.
• Figure 4: The ratio $(d\sigma^{\textrm{LP}}_{\rm NLO}/dp_T) / (d\sigma_{\rm NLO}/dp_T)$ for the polarized ${}^3P_1^{[1]}$ and ${}^3P_2^{[1]}$ channels in the process $p p \to H + X$ at $\sqrt{s}=7$ TeV and $|y|<1.2$. $h$ is the helicity of the $Q \bar{Q}$ pair in the final state.
• Figure 5: The ratio $(d\sigma^{{\rm LP+NLO}}/dp_T) / (d\sigma_{\rm NLO}/dp_T)$ for the ${}^1S_0^{[8]}$, ${}^3P_J^{[8]}$, and ${}^3S_1^{[8]}$ channels with unpolarized final states in the process $p p \to H + X$ at $\sqrt{s}=7$ TeV and $|y|<1.2$.