Measurement of the top quark pair production cross section in PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.36 TeV

The CMS experiment reports the first measurement of the inclusive top quark pair production cross section in lead-lead collisions at $\sqrt{s_\mathrm{NN}}$ = 5.36 TeV, finding results consistent with next-to-next-to-leading order perturbative QCD predictions and providing the first investigation of top quark production dependence on collision impact parameter.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. Usually, scientists smash two tiny protons together. But in this specific study, the CMS experiment decided to smash two massive lead nuclei (PbPb) together. Think of it as the difference between crashing two ping-pong balls versus crashing two bowling balls made of trillions of atoms.

The goal of this paper is to find something very specific and very heavy inside that chaotic crash: the top quark.

The Challenge: Finding a Needle in a Haystack

The top quark is the heaviest known elementary particle. It's like the "king" of the particle world. However, it's incredibly rare to make one, and it decays (falls apart) almost instantly.

In a lead-lead collision, the environment is incredibly messy. It's like trying to spot a single, specific type of firefly in a stadium during a thunderstorm, while the stadium is also on fire. There are billions of other particles flying around (the "haystack"), making it very hard to see the top quark (the "needle").

Previous attempts to find top quarks in these heavy collisions were like trying to find that firefly with a dim flashlight; they found some evidence, but the data was too fuzzy to be sure.

The New Approach: A Smarter Searchlight

This paper reports the first successful, clear measurement of top quark pairs produced in lead-lead collisions at a new, higher energy level (5.36 TeV). They used data collected in 2023, which is about the same amount of "crash data" as previous studies, but with a much better toolkit.

Here is how they did it, using simple analogies:

1. The "Dilepton" Signature: When a top quark is created, it almost immediately splits into a W boson and a bottom quark. The W boson then decays into a "lepton" (an electron or a muon). Since a top quark pair creates two W bosons, the team looked for events where two clean, high-energy leptons appeared. This is like looking for two specific, bright blue sparks in a cloud of gray smoke.
2. The "B-Jet" Clue: The other half of the top quark's decay is a "bottom quark," which turns into a spray of particles called a "jet." The team used a new, super-smart AI tool (called a "multivariate discriminator") to identify these specific "bottom jets." It's like having a detector that can smell the specific scent of the needle amidst the hay.
3. The "Centrality" Check: The researchers didn't just look at all crashes. They looked at how "head-on" the collisions were.
   • Central collisions: The two lead balls smash dead center (like two cars hitting bumper-to-bumper).
   • Semicentral collisions: They graze each other (like a glancing blow).
   • They measured the top quark production in both scenarios to see if the "impact parameter" (how hard they hit) changed the results.

The Results: A Clear Victory

The team successfully counted the top quark pairs and measured how often they are produced (the "cross-section").

• The Count: They found that top quark pairs are produced at a rate of about 3.42 microbarns. (Think of a microbarn as a tiny unit of probability; it's a very small number, meaning these events are rare).
• The Match: This number matches perfectly with the theoretical predictions made by physicists using complex math (Quantum Chromodynamics). It's like predicting exactly how many times a coin will land on heads after a million flips, and the actual result matches the math.
• The Ratio: They also measured the ratio of top quark production to another common process called "Drell-Yan" (which produces pairs of electrons or muons). This ratio acts as a control check, and it also matched the theory.

Why This Matters (According to the Paper)

The paper states that this measurement is a "powerful probe" for two main things:

1. Nuclear Gluon Density: It helps scientists understand how the "glue" (gluons) that holds the nucleus together is distributed inside a heavy lead atom.
2. The Quark-Gluon Plasma (QGP): When lead nuclei smash, they create a super-hot soup of particles called the Quark-Gluon Plasma. By seeing how the top quark (and its decay products) travels through this soup, scientists can learn about how energy is lost in this extreme environment (a phenomenon called "jet quenching").

The Bottom Line

This paper is a milestone because it proves that we can now reliably "see" the heaviest particle in the universe even when it's buried inside the most chaotic, heavy-ion collisions. It's the first time the CMS experiment has clearly observed this process in lead-lead collisions, moving from "maybe we saw it" to "we definitely measured it."

The results confirm that our current understanding of particle physics (the Standard Model) holds up even in these extreme, high-energy, heavy-ion environments.

Technical Summary

1. Problem and Motivation

The production of top quark pairs ($t\bar{t}$) in heavy-ion collisions serves as a unique probe for understanding the nuclear environment created in lead-lead (PbPb) collisions at the Large Hadron Collider (LHC).

• Nuclear Parton Distribution Functions (nPDFs): Top quarks are produced primarily via gluon-gluon fusion. Measuring their production rate in nuclei allows physicists to constrain the gluon density within the nucleus at high virtualities, testing models of nuclear shadowing and antishadowing.
• Quark-Gluon Plasma (QGP) Effects: While top quarks decay before the QGP fully forms, their decay products (specifically $b$-jets) traverse the medium. Studying $t\bar{t}$ production helps investigate final-state effects like "jet quenching" (parton energy loss).
• Previous Limitations: Earlier measurements in PbPb collisions (at $\sqrt{s_{NN}} = 5.02$ TeV) were limited by low statistical precision (integrated luminosity of $\sim 1.7-1.9$ nb$^{-1}$), preventing precise constraints on nPDFs or detailed studies of impact parameter dependence.
• Goal: This paper reports the first inclusive measurement of the $t\bar{t}$ cross section in PbPb collisions at the higher LHC Run 3 energy of $\sqrt{s_{NN}} = 5.36$ TeV, utilizing a larger dataset ($1.58$ nb$^{-1}$) and advanced analysis techniques to reduce uncertainties.

2. Methodology

Data and Simulation

• Dataset: Data collected by the CMS experiment in 2023, corresponding to an integrated luminosity of 1.58 nb$^{-1}$.
• Signal Channel: The analysis focuses on the dilepton decay channel ($t\bar{t} \to (W^+b)(W^-b) \to (\ell^+\nu_\ell b)(\ell^-\bar{\nu}_\ell b)$), where $\ell$ represents electrons or muons. This channel offers the cleanest signature despite a low branching fraction ($\sim 4\%$ for $e/\mu$), providing high purity ($>95\%$).
• Monte Carlo (MC): Signal and background samples were generated using NLO matrix element generators (MADGRAPH5_aMC@NLO, POWHEG) interfaced with PYTHIA 8 for parton showering. Nuclear effects were modeled using EPPS21 nPDFs. Backgrounds (Drell-Yan, $W$+jets, single top, diboson, multijets) were simulated and embedded into inelastic PbPb events using the HYDJET generator to model the underlying event.

Event Selection and Reconstruction

• Triggers: Minimum-bias and single-muon triggers were used.
• Lepton Selection: Events required two isolated leptons ($p_T > 20$ GeV). Electrons were restricted to $|\eta| < 2.5$ (excluding the transition region), and muons to $|\eta| < 2.4$.
• Identification:
  • Electrons: Identified using a Boosted Decision Tree (BDT) trained on QCD and $t\bar{t}$ simulations, achieving 95% efficiency with $<4\%$ misidentification.
  • Muons: Selected using standard "tight" criteria.
  • Isolation: A dedicated BDT isolation algorithm was developed using the "soft killer" method to mitigate the high particle multiplicity in PbPb collisions, ensuring 90% efficiency independent of collision centrality.
• Jet Reconstruction: Jets were clustered using the anti-$k_T$ algorithm ($R=0.3$).
• $b$-tagging: A novel multivariate algorithm called "Unified Particle Transformer" (UPART) was employed. Trained specifically for heavy-ion collisions, UPART uses transformer architecture to analyze jet constituents, reducing the misidentification rate by an order of magnitude compared to Run 2 algorithms. Three working points (loose, intermediate, tight) were defined; the intermediate point (80% efficiency) was used as default.

Signal Extraction and Background Estimation

• Multivariate Analysis: Three separate BDT classifiers were trained for different final states ($e^+e^-$, $\mu^+\mu^-$, and $e^\mp\mu^\pm$) to distinguish signal from background. Inputs included lepton kinematics, dilepton system properties ($p_T$, mass, sphericity), and $b$-jet multiplicity (0, 1, or $\ge 2$).
• Backgrounds:
  • Drell-Yan (DY): Normalization was left to float in the final fit.
  • Non-prompt Leptons: Estimated using an event-mixing technique, pairing leptons from different events with similar centrality and kinematic properties. This method significantly reduced statistical uncertainty.
• Fitting: A simultaneous fit was performed across multiple categories (flavor, charge, $b$-jet multiplicity, centrality) using the COMBINE tool. The signal strength $\mu = \sigma_{meas}/\sigma_{th}$ was extracted.

3. Key Contributions

1. First Inclusive Measurement at 5.36 TeV: This is the first observation of $t\bar{t}$ production in PbPb collisions at the LHC's highest heavy-ion energy, utilizing the 2023 Run 3 dataset.
2. Advanced Machine Learning Techniques:
   • Implementation of UPART for heavy-flavor jet tagging in the high-multiplicity heavy-ion environment.
   • Development of BDT-based lepton isolation and identification to handle the dense underlying event.
   • Use of event mixing for robust non-prompt lepton background estimation.
3. Centrality Dependence: For the first time, the analysis measured $t\bar{t}$ and Drell-Yan cross sections separately for central (0–10%) and semicentral (10–90%) collisions, investigating the dependence on the impact parameter.
4. Ratio Measurement: The ratio $R_{t\bar{t}/DY} = \sigma_{t\bar{t}} / \sigma_{DY}$ was measured to cancel common systematic uncertainties (like luminosity) and directly probe the relative gluon vs. quark content of nuclear PDFs.

4. Results

Cross Section Measurements

The measured inclusive cross sections are:

• Top Pair Production: $\sigma_{t\bar{t}} = 3.42^{+0.54}_{-0.51} (\text{stat}) ^{+0.50}_{-0.43} (\text{syst}) \, \mu\text{b}$.
• Drell-Yan Production ($m_{\ell\ell} > 10$ GeV): $\sigma_{DY} = 397 \pm 3 (\text{stat}) ^{+27}_{-25} (\text{syst}) \, \mu\text{b}$.
• Ratio: $R_{t\bar{t}/DY} = 0.0086^{+0.0014}_{-0.13} (\text{stat}) ^{+0.0011}_{-0.0010} (\text{syst})$.

Comparison with Theory

• The measured $\sigma_{t\bar{t}}$ is consistent with Next-to-Next-to-Leading Order (NNLO) perturbative QCD predictions using various nPDF sets (EPPS21, nNNPDF3.0, TUJU21).
• The $R_{t\bar{t}/DY}$ ratio is also compatible with NNLO predictions.
• The results show no significant deviation from the expectation that nuclear effects (shadowing/antishadowing) are mild in the kinematic region probed.

Centrality Dependence

• The cross sections were measured for 0–10% (central) and 10–90% (semicentral) collisions.
• The ratio $R_{t\bar{t}/DY}$ was found to be independent of centrality, suggesting that the nuclear modification of the gluon density (which drives $t\bar{t}$) and the quark density (which drives DY) scale similarly with the impact parameter in this kinematic regime.

Significance

• The signal strength was extracted as $\mu = 0.93^{+0.15}_{-0.14} (\text{stat}) ^{+0.14}_{-0.12} (\text{syst})$.
• The observation of the $t\bar{t}$ signal has a statistical significance exceeding 5 standard deviations relative to the background-only hypothesis.

5. Significance and Impact

• Precision Physics in Heavy Ions: This analysis demonstrates that top quark physics can be performed with high precision in the extreme environment of heavy-ion collisions, overcoming challenges posed by the large hadronic background.
• Constraints on nPDFs: While current experimental uncertainties ($\sim 20\%$) do not yet fully discriminate between different nPDF sets, the results provide crucial new constraints, particularly for the gluon distribution at high momentum fractions ($x$) and high virtualities ($Q^2$).
• Future Probes: The measurement establishes top quark production as a robust probe for future studies of initial-state nuclear effects and final-state interactions (jet quenching) in the QGP. The ability to measure centrality dependence opens new avenues for studying the geometry of the collision and the path-length dependence of parton energy loss.
• Methodological Advancement: The successful application of transformer-based jet tagging (UPART) and advanced multivariate background estimation sets a new standard for heavy-ion analyses in the high-luminosity era of the LHC.