J/ψ Yield Measurement in Collider Experiments

• J/ψ yield measurement is a method that quantifies the production of J/ψ mesons in collisions by evaluating their number or cross section within defined kinematic ranges.
• It employs advanced techniques such as invariant-mass analysis, luminosity normalization, and detailed GEANT-based simulations to correct for detector response and systematic uncertainties.
• Accurate yield extraction provides essential benchmarks for QCD models and insights into nuclear modification effects, multi-parton interactions, and quark-gluon plasma dynamics.

The measurement of the J/$\psi$ yield—defined as the number or cross section of produced J/$\psi$ mesons in a given collision system and kinematic range—is a foundational operation in experimental hadron and nuclear physics. It underpins studies of heavy quarkonium production mechanisms, tests of perturbative and nonperturbative QCD, and probes of nuclear and hot-medium effects. J/$\psi$ yield measurements are conducted in a wide range of environments: e$^+$e$^-$ colliders (charmonium threshold production), fixed-target hadronic collisions, high-energy proton–proton and heavy-ion collisions at colliders such as RHIC and the LHC, and in proton–nucleus and nucleus–nucleus reactions relevant to the study of the Quark-Gluon Plasma (QGP) and cold nuclear matter (CNM). Common to all contexts is the requirement for precise yield extraction, luminosity normalization, detector-response correction (acceptance × efficiency), and control of systematic uncertainties.

1. Experimental Techniques and Detector Architectures

J/$\psi$ yield measurements are implemented in several major experimental configurations:

• Central and forward detectors: For example, ALICE employs a central barrel (|η| < 0.9) with the ITS and TPC for dielectron (e$^+$e$^-$) measurements, and a dedicated forward muon spectrometer (2.5 < y < 4) with layered absorbers, tracking stations, and muon trigger chambers for dimuon (μ$^+$μ$^-$) detection (Arnaldi, 2011). PHENIX and STAR at RHIC use both central and forward arm geometries, with spectrometers optimized for muon tracks (PHENIX: 1.2 < |y| < 2.2) or electron pairs (STAR: |y| < 1).
• Trigger and data selection: J/$\psi$ triggers typically combine a minimum-bias requirement (e.g., SPD/VZERO signals for ALICE; BBC/MB triggers at RHIC) with more selective electron/muon triggers at higher $p_T$ or multiplicities. At BESIII and B-factories, inclusive event selection relies on global energy/multiplicity triggers and dedicated resonance settings (Ablikim et al., 2016).
• Luminosity determination: The normalization to integrated luminosity uses calibrated reference processes (QED, Vernier scans, or beam-beam counters), with systematic uncertainties ranging from a few to several percent depending on the experiment.
• Acceptance and efficiency evaluation: All experiments perform detailed GEANT-based Monte Carlo simulations to extract the product $A\times\varepsilon(p_T,y)$, quantifying detector geometry, tracking, signal identification (d$E$/d$x$, TOF, calorimetry, muon ID), and trigger logic. Corrections for polarization (notably, the acceptance depends on $J/\psi$ spin alignment) are included as sources of systematic uncertainty (Arnaldi, 2011, Collaboration, 2023).(Trzeciak, 2014)

2. Yield Extraction Methods and Signal/Background Separation

The extraction of the J/$\psi$ raw yield in each kinematic bin follows specific procedures tailored to the decay channel and background composition:

• Invariant-mass techniques: In both dielectron and dimuon channels, candidate pairs are reconstructed and their invariant mass $m_{\ell\ell}$ filled in bins of $p_T$, $y$, centrality, or event multiplicity. The raw signal count $N_{J/\psi}^{\mathrm{raw}}$ is extracted by:
  • Dielectrons: like-sign background subtraction plus bin counting at the J/$\psi$ peak.
  • Dimuons: fitting $m_{\mu\mu}$ with a Crystal-Ball (or double-Gaussian) function for the signal and empirical forms (double exponential, polynomial) for the background (Arnaldi, 2011, Li, 2024).
  • For high-background environments (low $p_T$ or high-multiplicity collisions), event-mixing and mixed-event or like-sign spectra are used to control combinatorial and correlated backgrounds (Massacrier, 2015).
• Differential Cross Section Calculation: For each $(p_T, y)$ bin,

$$\frac{d^2\sigma_{J/\psi}}{dp_T dy} = \frac{N_{J/\psi}(p_T,y)}{L_{\rm int}\ \mathrm{BR}(J/\psi\to\ell^+\ell^-)\ (A\times\varepsilon)(p_T,y)\ \Delta p_T\ \Delta y}$$

with analogous expressions for integrated or per-event yields in heavy-ion collisions and for exclusive production in UPCs (Arnaldi, 2011, Lofnes, 2020, Feng et al., 2015, collaboration et al., 2014, collaboration et al., 2024).

• Polarization Effects: Variations in $J/\psi$ spin alignment impact acceptance. Experiments such as STAR and ATLAS include the change in $A\times\varepsilon$ across polarization scenarios as a systematic uncertainty, sometimes parametrized via $\lambda_\theta$ or other angular coefficients (Trzeciak, 2014, Collaboration, 2023).

3. Systematic Uncertainties and Correction Factors

The dominant sources of systematic uncertainty include:

Source	Typical Magnitude	Description/Origin
Acceptance × efficiency ($A\varepsilon$)	5–20%	MC kinematics, tracking/PID performance
Signal extraction	3–10%	Fit model, mass window, background method
Luminosity	3–10%	Calibration, reference process normalization
Branching Ratio	<1%	PDG value for $J/\psi\to\ell^+\ell^-$
Polarization assumption	up to 15%	Extreme spin-alignment scenarios
Physics model input	few % up to 10%	MC event generator, PDF choice, etc.

A total point-to-point systematic of 10–20% is typical in modern collider experiments (Arnaldi, 2011, Trzeciak, 2014, Collaboration, 2023).

4. Numerical Results: Cross Sections and Yields in Key Experiments

Distinct collision systems and experimental configurations yield characteristic results:

ALICE (pp at √s = 2.76, 7 TeV):

Channel	√s (TeV)	Rapidity	$N_{J/\psi}$	$\sigma_{J/\psi}$ (μb)
Dielectrons	7		y	< 0.9
Dimuons	7	2.5 < y < 4	$1924\pm77$	$6.31\pm0.25\pm0.80^{+0.95}_{-1.96}$
Dielectrons	2.76		y	< 0.9
Dimuons	2.76	2.5 < y < 4	$1287\pm48$	$3.46\pm0.13\pm0.42^{+0.55}_{-1.11}$

Measurements are performed down to $p_T=0$. The $p_T$-differential yields follow a parametrization

$$\frac{d^2\sigma}{dp_T\,dy} \propto \frac{p_T}{\left[1+(p_T/p_0)^2\right]^n}$$

with $\langle p_T^2\rangle$ exhibiting a logarithmic increase with $\sqrt{s}$, consistent from fixed-target to LHC energies. Rapidity-differential yields increase linearly with $\sqrt{s}$, and high-multiplicity events manifest a linear rise in relative yield, suggesting multi-parton dynamics even in $pp$ (Arnaldi, 2011).

PHENIX/STAR (RHIC, √s = 200, 500 GeV):

• Yields are reported as double-differential cross sections $d^2\sigma/dy\,dp_T$, e.g., for $|y|<1$, $p_T=1$ GeV/$c$: $(d^2\sigma/2\pi p_T\,dp_T\,dy)\approx 10$ nb/(GeV/$c$)$^2$ at 200 GeV, declining by orders of magnitude at high $p_T$. Systematic errors from acceptance, signal extraction, and trigger are typically 10–15% (Trzeciak, 2014, Trzeciak, 2015).

BESIII (e$^+$e$^-$ at resonance):

• For inclusive J/$\psi$, $$N_{J/\psi}^{2012}=(1086.90\pm 0.04_{\rm stat}\pm 6.0_{\rm syst})\times10^6$$ and $$N_{J/\psi}^{2009}=(223.72\pm 0.01_{\rm stat}\pm1.4_{\rm syst})\times10^6$$, with total systematic uncertainty 0.6% (Ablikim et al., 2016).

LHCb/ATLAS/CMS (Exclusive and Prompt/Non-prompt J/$\psi$):

• LHCb, e.g., at 13 TeV: $$\sigma_{pp\to J/\psi\to\mu^+\mu^-}(2.0<y<4.5) = 400 \pm 2_{\rm stat} \pm 5_{\rm syst} \pm12_{\rm lumi}$$ pb (collaboration et al., 2024); ATLAS, e.g., for $|y|<2.0$ and $p_T > 8$ GeV: prompt and non-prompt double-differential cross sections are measured with 5–10% precision per bin. Spin-alignment, fit-model, and efficiency uncertainties dominate systematics (Collaboration, 2023).

5. Specialized Yield Contexts: Heavy-Ion, Fixed-Target, and Photoproduction

• Heavy-Ion Collisions and Nuclear Modification Factors: In $A$+$A$ systems, J/$\psi$ yield per event, normalized to vacuum cross sections and geometry (e.g., $\langle T_{AA} \rangle$ from Glauber fits), yields the nuclear modification factor $R_{AA}(p_T,y)$. Peripheral Pb–Pb at $\sqrt{s_{NN}}=2.76$ TeV shows an unexpected strong enhancement of very-low-$p_T$ J/$\psi$ yield ($R_{AA}\sim7$ at $p_T<0.3$ GeV/$c$ in 70–90% centrality), interpreted as evidence for coherent photoproduction at $b<2R_A$ (Massacrier, 2015, Collaboration, 2015).
• Low-Energy Nuclear Collisions (SPS, FAIR): Model yields using a Glauber ansatz with effective absorption cross section $\sigma_{abs}^{J/\psi}(\sqrt{s})$ provide "cold nuclear matter" baselines. For minimum-bias Pb+Pb at $\sqrt{s_{NN}}=7.6$ GeV, the expected per-event yield is $1.2\times10^{-7}$ with substantial extrapolation uncertainties. Deviations from baseline will be diagnostic of QGP suppression or regeneration (Chatterjee et al., 2022).
• Fixed Target and SeaQuest (120 GeV pp, pd): $d\sigma/dx_F$ and $d\sigma/dp_T^2$ are extracted per nucleon, with acceptance/effectivity corrections and precise luminosity normalization; in SeaQuest, average $\langle p_T^2\rangle \approx 0.71$ GeV$^2$ and forward $R_{pd}\approx 1.05$ reflect the mixture of $gg$ fusion and $q\bar{q}$ annihilation (Leung et al., 2024).
• Exclusive Photoproduction: In events with strict exclusivity requirements (no extra tracks, small $p_T$), e.g. in LHCb, the efficiency-corrected yield is normalized by the effective luminosity (taking into account the single-interaction fraction), and differential and integrated cross sections are reported. Systematic uncertainties typically include component yields from fiducial fits, veto efficiencies, and background subtraction (collaboration et al., 2024, collaboration et al., 2014).

6. Implications for Theory and Model Benchmarking

Measured differential yields and their systematics are critical benchmarks for QCD-based models. At high $p_T$, NLO NRQCD using global fits of long-distance matrix elements (LDMEs) reproduce LHC and RHIC data within 30–50% uncertainties. At low $p_T$, color-evaporation models and models with gluon saturation are also tested; at fixed-target energies, yield decompositions clarify the relative weight of $gg$ fusion and $q\bar{q}$ annihilation channels (Arnaldi, 2011, Feng et al., 2015, Leung et al., 2024). Multiplicity-dependent yields in $pp$ require explicit multi-parton interaction modeling (as in PYTHIA with MPI turned on) (Li, 2024, Trzeciak, 2015).

For heavy-ion studies, deviation of measured yields from "CNM baseline" yield predictions (Glauber + effective absorption) reveal the presence of hot-medium suppression or regeneration. The precise measurement of $J/\psi$ yields in reference systems (e$^+$e$^-$, $pp$, $pA$) is thus essential to quantify anomalous effects such as QGP color screening or recombination.

7. Current Challenges and Opportunities

J/$\psi$ yield measurements face challenges in:

• Unfolding acceptance and efficiency with minimal model dependence, particularly for polarization and kinematic distributions.
• Achieving sub-10% systematics in high-multiplicity and heavy-ion environments.
• Isolating prompt, non-prompt, and feed-down contributions in collider experiments through lifetime fits and mass-window analyses.
• Extending sensitivity to low $p_T$ and exclusive production, including coherent and photoproduction mechanisms, which provide unique probes of nuclear PDFs and initial-state gluon densities (Massacrier, 2015, Collaboration, 2015).

The continuing refinement of yield measurement methodologies and systematic control, coupled with advances in theoretical modeling and higher-statistics datasets, will further advance the quantitative study of quarkonium production and its use as a probe of QCD matter.