[Paper Review] A short theoretical review of charmonium production

An-Ping Chen, Yan-Qing Ma+1 more|arXiv (Cornell University)|Sep 9, 2021

High-Energy Particle Collisions Research4 citations

TL;DR

This paper reviews theoretical frameworks—particularly NRQCD factorization—for charmonium production in high-energy collisions, comparing predictions with experimental data across $pp$, $e^+e^-$, $ep$, and $γγ$ processes. Despite NLO improvements, tensions remain in describing yields, polarization, and universality of long-distance matrix elements (LDMEs), highlighting persistent challenges in QCD modeling of quarkonium production.

ABSTRACT

In this paper, we review the current status of the phenomenological study of quarkonium production in high energy collisions. After a brief introduction of several important models and effective field theories for quarkonium production, we discuss the comparisons between theoretical predictions and experimental measurements.

Motivation & Objective

• To assess the current status of phenomenological models for quarkonium production in high-energy collisions.
• To identify persistent theoretical-experimental discrepancies in charmonium production, especially regarding polarization and long-distance matrix elements (LDMEs).
• To evaluate the performance of NRQCD factorization at NLO in describing inclusive yields and polarization observables.
• To explore the limitations of existing frameworks and the potential of emerging approaches like soft gluon factorization (SGF).

Proposed method

• Reviews five major theoretical frameworks: color evaporation model (CEM), color singlet model (CSM), NRQCD factorization, fragmentation function approach, and soft gluon factorization (SGF).
• Applies NRQCD factorization with leading-order (LO) and next-to-leading-order (NLO) QCD corrections to calculate partonic cross sections for $pp$, $e^+e^-$, $ep$, and $γγ$ processes.
• Uses global fits of LDMEs to constrain nonperturbative matrix elements in NRQCD, incorporating data from LHC, HERA, and DELPHI.
• Compares theoretical predictions with experimental data on $J/\psi$ yields and polarization from CDF, PHENIX, STAR, CMS, ATLAS, ALICE, LHCb, H1, ZEUS, and DELPHI.
• Analyzes the role of resolved photon contributions in $ep$ and $γγ$ collisions using photon flux and parton distribution functions.
• Evaluates the impact of relativistic corrections and convergence issues in velocity expansion via the SGF approach as a potential solution.

Experimental results

Research questions

• RQ1 Why do NRQCD predictions for $J/\psi$ polarization in $ep$ and $\gamma\gamma$ collisions show discrepancies with HERA data, especially at high transverse momentum?
• RQ2 To what extent do LDMEs extracted from different datasets (e.g., LHC vs. HERA) agree, and what does this imply for the universality of NRQCD?
• RQ3 Why does the NLO NRQCD prediction for $J/\psi$ production in $e^+e^-$ via $γ\gamma$ fusion fall significantly below DELPHI data, and what causes the ${{}^{3}P_{0}^{[8]}}$ contribution cancellation?
• RQ4 Can the soft gluon factorization (SGF) approach resolve the convergence and universality issues in NRQCD by better controlling relativistic corrections?
• RQ5 How well does the combination of NRQCD and CGC effective theory describe quarkonium production across the full transverse momentum spectrum in $pp$ collisions?

Key findings

• NRQCD factorization at NLO provides a qualitatively correct description of inclusive charmonium yields across $pp$, $e^+e^-$, $ep$, and $γγ$ processes.
• The $J/\psi$ polarization prediction in $ep$ photoproduction is approximately unpolarized at high $p_T$, consistent with H1 data but inconsistent with ZEUS data showing transverse polarization at $z \approx 1$.
• NLO NRQCD calculations for $\gamma\gamma$ fusion at $e^+e^-$ colliders underpredict DELPHI data by a factor of several due to destructive interference between ${{}^{1}S_{0}^{[8]}}$ and ${{}^{3}P_{0}^{[8]}}$ LDMEs, particularly due to the negative value of $\langle{\mathcal{O}}^{J/\psi}({{}^{3}P_{0}^{[8]}})\rangle$.
• Global fits of LDMEs from diverse datasets yield inconsistent results, indicating a lack of universality and challenging the robustness of NRQCD predictions.
• The polarization puzzle and LDME universality problem persist, likely due to poor convergence of the velocity expansion in NRQCD.
• The soft gluon factorization (SGF) approach is proposed as a promising alternative with better-controlled relativistic corrections, potentially resolving current inconsistencies in NRQCD.