Inclusive $ψ(2S)$ production at midrapidity in pp collisions at $\sqrt{s} = 13$ TeV

This paper presents the first measurement of inclusive $\psi(2S)$ production at midrapidity in pp collisions at $\sqrt{s} = 13$ TeV using the ALICE detector, reporting the transverse-momentum differential cross section and its ratio to J/$\psi$ production, which reveals a mild rise in the ratio with increasing $p_{\rm T}$ and is compared with NRQCD and ICEM theoretical models.

The Gist

The Big Picture: Catching Rare Cosmic Fireflies

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle blender. Scientists smash protons together at nearly the speed of light to see what tiny fragments fly out. Usually, these fragments are common particles like pions or kaons. But sometimes, the collision creates something special: a charmonium particle.

Think of a charmonium particle as a tiny, exotic atom made of a "charm" quark and an "anti-charm" quark holding hands. They are like a couple dancing in a whirlwind.

There are two main "dancers" in this family:

1. The J/ψ: The popular, well-known celebrity. Scientists have studied this one for decades.
2. The $\psi(2S)$: The celebrity's slightly more energetic, harder-to-find cousin. It's heavier and more excited.

The Goal of this Paper:
For the first time, the ALICE team (a group of scientists using a specific detector called ALICE) managed to catch a clear view of this "exotic cousin" ($\psi(2S)$) right in the middle of the collision zone (called "midrapidity") and at lower speeds than ever before. They wanted to see how often it appears compared to its famous cousin (J/ψ) and check if our theories about how the universe works are correct.

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The Challenge: Finding a Needle in a Haystack

The Problem:
When you smash protons together, you get billions of particles. Finding a $\psi(2S)$ is like trying to find a specific, rare firefly in a stadium full of regular moths. Most of the time, the detector gets overwhelmed by the "noise" (the common particles).

The Solution: The "VIP Bouncer" (The TRD Trigger)
Usually, the detector records everything (like a security camera recording every person entering a stadium). But for this experiment, the scientists used a special "VIP Bouncer" called the Transition Radiation Detector (TRD).

• How it works: The TRD is like a bouncer who only lets people with a specific "glow" (high-energy electrons) into the VIP section.
• The Result: Instead of recording every single collision, the detector only saved the events where this "glow" was seen. This made the data set much smaller but much richer in the rare particles they were looking for. It's like filtering a video feed to only show frames where a celebrity appears, ignoring all the background crowd.

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The Discovery: A New Perspective

1. Lowering the Speed Limit
Previous experiments could only see these particles when they were zooming very fast (high momentum). This new study managed to see them even when they were moving more slowly (between 4 and 16 GeV/c).

• Analogy: Imagine you've only ever seen a cheetah running at full sprint. This study is the first time someone successfully photographed the cheetah while it was jogging or walking. It gives a more complete picture of the animal's behavior.

2. The Ratio Game
The scientists counted how many $\psi(2S)$ cousins they found compared to the J/ψ celebrities.

• The Finding: As the particles move faster, the ratio of cousins to celebrities slowly goes up.
• Why it matters: It's like noticing that in a crowded party, the more energetic the music gets, the more likely you are to see the "cool cousin" dancing next to the "famous uncle." This trend helps physicists understand the rules of the dance floor.

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The Theory Check: Are the Rules Right?

Physicists have two main rulebooks (theories) for predicting how these particles are made:

1. NRQCD (The Detailed Rulebook): This theory breaks the process down into tiny, precise steps.
   • The Result: The data matched this rulebook almost perfectly. The predictions were right on the money.
2. ICEM (The Simplified Rulebook): This theory uses a broader, more general approach (like a "rule of thumb").
   • The Result: It was okay, but it predicted the ratio of cousins to celebrities would stay flat (unchanging). The real data showed the ratio rising. So, the simplified rulebook missed a subtle detail.

The Takeaway: The universe seems to follow the more complex, detailed rulebook (NRQCD) rather than the simple shortcut.

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Why Should You Care?

You might ask, "Who cares about a heavy cousin of an atom?"

• Understanding the "Glue": These particles are made of quarks held together by the "strong force" (the glue of the universe). Studying them helps us understand how matter is built from the ground up.
• The "Quark-Gluon Plasma": In the early universe (just after the Big Bang), matter existed as a hot soup called Quark-Gluon Plasma. Heavy-ion collisions (smashing big atoms together) recreate this soup. To understand the soup, we first need to know how the ingredients behave in a normal setting (like the proton collisions in this paper). This paper provides the "baseline" data needed to understand the extreme conditions of the early universe.

Summary in One Sentence

The ALICE team used a clever electronic filter to find a rare, heavy particle ($\psi(2S)$) moving at moderate speeds, proving that our most detailed theories of particle physics are correct and helping us better understand how the building blocks of the universe stick together.

Technical Summary

1. Problem and Motivation

Charmonium states (bound states of a charm and anti-charm quark, $c\bar{c}$), such as the $J/\psi$ and $\psi(2S)$, serve as critical probes for understanding Quantum Chromodynamics (QCD) and the mechanisms of heavy-flavor hadronization.

• Theoretical Challenges: While perturbative QCD describes the hard production of the $c\bar{c}$ pair, the non-perturbative transition (hadronization) into a specific quarkonium state is complex. Models like the Color Singlet Model (CSM), Non-Relativistic QCD (NRQCD), and the Color Evaporation Model (CEM) attempt to describe this. However, recent observations of enhanced heavy-flavor baryon production suggest that hadronization may depend on the collision environment, challenging the assumption of universal fragmentation.
• Experimental Gap: Previous measurements of inclusive $\psi(2S)$ production at midrapidity ($|y| < 0.9$) at the LHC were limited to higher transverse momenta ($p_T > 6.5$ GeV/c for CMS, $p_T > 10$ GeV/c for ATLAS) or lower collision energies. There was a lack of data in the intermediate-to-low $p_T$ region (4–8 GeV/c) at $\sqrt{s} = 13$ TeV, which is crucial for testing the $p_T$ dependence of production mechanisms and the ratio between excited ($\psi(2S)$) and ground ($J/\psi$) states.
• Objective: To measure the inclusive $p_T$-differential production cross-section of $\psi(2S)$ mesons at midrapidity for the first time at $\sqrt{s} = 13$ TeV and to determine the $\psi(2S)$-to-$J/\psi$ cross-section ratio, extending the accessible $p_T$ range down to 4 GeV/c.

2. Methodology

Data Sample and Trigger

• Collision System: Proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV.
• Detector: The ALICE detector at the LHC.
• Trigger Strategy: Unlike previous inclusive $J/\psi$ measurements that used Minimum Bias (MB) triggers, this analysis utilized a Level-1 Transition Radiation Detector (TRD) trigger.
  • The TRD trigger required a single electron or positron with $p_T \geq 2$ GeV/c.
  • This significantly enriched the sample of events containing quarkonium decays, providing an enhancement factor of $\approx 34$ compared to MB triggers.
  • Integrated Luminosity: $1.7 \pm 1.8\% \text{ (syst.)} \text{ pb}^{-1}$.

Event Selection and Reconstruction

• Decay Channel: Both $J/\psi$ and $\psi(2S)$ were reconstructed via their dielectron decay channels ($e^+e^-$).
• Tracking: Tracks were reconstructed using the Inner Tracking System (ITS) and Time Projection Chamber (TPC), covering $|\eta| < 0.9$.
• Quality Cuts:
  • Tracks required hits in the ITS and TPC, with specific requirements on the Silicon Pixel Detector (SPD) to suppress photon conversion backgrounds.
  • Distance of Closest Approach (DCA) cuts were applied to select primary vertices.
  • Particle Identification (PID) was performed using specific energy loss ($dE/dx$) in the TPC ($n\sigma_e$) and TRD likelihood.
• Signal Extraction:
  • Invariant mass distributions ($m_{ee}$) of opposite-sign pairs were analyzed.
  • Background Subtraction: Uncorrelated combinatorial background was estimated using the Mixed-Event (ME) technique.
  • Fitting: The remaining distribution was fitted with signal templates (from Monte Carlo) for $J/\psi$ and $\psi(2S)$ and a second-order polynomial for correlated background (heavy-flavor decays).
  • Significance: The $\psi(2S)$ signal was observed with a statistical significance of $3.9\sigma$ even in the lowest $p_T$ bin ($4 < p_{ee}^T < 6$ GeV/c).

Corrections and Systematics

• Efficiency Corrections: The raw yields were corrected for acceptance ($A$) and efficiency ($\epsilon$), including tracking, PID, mass window, and TRD-trigger efficiency.
• Monte Carlo (MC): Simulations used PYTHIA 6.4 (Perugia 2011 tune) with embedded $J/\psi$ and $\psi(2S)$ mesons. The $p_T$ distributions were iteratively reweighted to match experimental data.
• Systematic Uncertainties: Evaluated for tracking, PID, signal extraction, fit functions, MC $p_T$ shape, and TRD-trigger efficiency. The total systematic uncertainty for the cross-section was calculated as the quadratic sum of individual sources (excluding branching ratios and luminosity).

3. Key Contributions

1. First Midrapidity Measurement at 13 TeV: This is the first measurement of inclusive $\psi(2S)$ production at midrapidity in $pp$ collisions at $\sqrt{s} = 13$ TeV.
2. Extended $p_T$ Range: The analysis extends the accessible $p_T$ range down to 4 GeV/c, bridging the gap between forward-rapidity measurements and high-$p_T$ measurements by ATLAS and CMS.
3. Consistent Ratio Measurement: By using the same dataset and analysis framework for both $J/\psi$ and $\psi(2S)$, the paper provides a highly consistent measurement of the $\psi(2S)$-to-$J/\psi$ cross-section ratio, minimizing correlated systematic uncertainties.
4. Trigger Innovation: Demonstrated the effectiveness of the TRD single-electron trigger for enhancing quarkonium yields in the intermediate $p_T$ region.

4. Results

Production Cross Section

• The $p_T$-differential inclusive $\psi(2S)$ production cross-section was measured in the range $4 < p_T < 16$ GeV/c.
• The data were well-described by a power-law function ($f(p_T) = K \times p_T / (1+(p_T/p_0)^2)^n$).
• Comparison with ATLAS: In the overlapping region ($8 < p_T < 16$ GeV/c), the ALICE results are fully consistent with inclusive measurements derived from ATLAS data.
• Rapidity Dependence: Comparing midrapidity results with previous forward-rapidity measurements [ALICE Ref 2] revealed a hardening of the $\psi(2S)$ spectrum at midrapidity (the ratio of mid-to-forward rapidity yields decreases with increasing $p_T$).

$\psi(2S)$-to-$J/\psi$ Ratio

• The ratio of the inclusive $\psi(2S)$ to $J/\psi$ cross-sections was found to be consistent with ATLAS results in the overlapping region.
• Trend: A mild rise in the $\psi(2S)$-to-$J/\psi$ ratio was observed as $p_T$ increases.
• Rapidity Independence: The ratio shows no significant dependence on rapidity within current uncertainties.

Comparison with Theoretical Models

• NRQCD (Non-Relativistic QCD): The NLO NRQCD calculations (including non-prompt contributions from beauty hadron decays via FONLL) describe the experimental data quantitatively over the entire $p_T$ range. The model predicts a rising ratio consistent with the data.
• ICEM (Improved Color Evaporation Model): The ICEM predictions are consistent with the absolute $\psi(2S)$ cross-section (though tending toward the lower edge) but fail to reproduce the rising trend of the $\psi(2S)$-to-$J/\psi$ ratio. ICEM predicts an almost flat ratio because it assumes $p_T$-independent production mechanisms for different quarkonium states, whereas the data show an increase.

5. Significance

• Validation of NRQCD: The results provide strong support for the NRQCD factorization framework, particularly its ability to describe the relative production rates of excited versus ground states across a wide $p_T$ range.
• Constraints on Hadronization: The observed rise in the $\psi(2S)$-to-$J/\psi$ ratio challenges models (like the standard ICEM) that assume strict universality in the fragmentation of $c\bar{c}$ pairs into different charmonium states. It suggests that higher-order QCD corrections or specific kinematic dependencies play a significant role.
• Baseline for Heavy-Ion Physics: These precise measurements in $pp$ collisions establish a robust baseline for studying charmonium suppression and regeneration in proton-nucleus and nucleus-nucleus collisions, where the Quark-Gluon Plasma (QGP) is formed.
• Low $p_T$ Physics: Extending the measurement down to 4 GeV/c allows for a more complete understanding of the transition region between soft and hard QCD processes.

In conclusion, this paper successfully extends the kinematic reach of charmonium measurements at the LHC, providing critical data that favors NRQCD predictions over the ICEM regarding the $p_T$ dependence of the $\psi(2S)$-to-$J/\psi$ ratio.