Recent measurements of top cross sections at CMS

This paper presents recent CMS measurements of inclusive and differential cross sections for top quark pair and single top quark production in proton-proton collisions at 5.02 TeV and 13.6 TeV, all of which are consistent with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle accelerator, essentially a giant cosmic racetrack where scientists smash protons together at nearly the speed of light. The goal? To recreate the conditions of the early universe and discover how the fundamental building blocks of nature behave.

This paper is a report card from the CMS experiment, one of the giant detectors sitting on that racetrack. The researchers are focusing on the top quark, which is the "heavyweight champion" of the particle world. It's the heaviest known fundamental particle, and because it's so massive and short-lived, it's like a celebrity that appears for a split second and then vanishes. Studying it helps scientists check if their current rulebook (the Standard Model) is correct or if there are hidden chapters they haven't written yet.

The paper covers two specific "races" or experiments the CMS team ran:

Race 1: The Top Quark Pair at a Lower Speed (5.02 TeV)

The Setup:
In 2017, the team ran the collider at a lower energy level (5.02 TeV). Think of this as a practice run on a quieter track with fewer cars (less "pileup" from other collisions). They collected data equivalent to 302 "petabytes" of collision events (though the unit here is inverse picobarns, a measure of how many collisions they saw).

The Strategy:
When two protons smash, they sometimes create a pair of top quarks (a top and an anti-top). These decay almost instantly into other particles, including electrons or muons (heavy cousins of electrons) and jets (sprays of particles).

• The Filter: The scientists acted like bouncers at a club. They only let in events that had exactly one electron or muon and at least three jets.
• The Sorting: They sorted these events into eight different "bins" based on how many jets and how many "b-jets" (jets containing bottom quarks, a signature of top quarks) they found.
• The Detective Work: In the messy bins where background noise (other random particle collisions) was high, they used a Random Forest algorithm. You can think of this as a team of digital detectives trained to spot the subtle differences between a real top-quark event and a fake one, much like a security system distinguishing between a real intruder and a shadow.

The Result:
They measured the "cross section," which is essentially the probability or the "target size" of this event happening. They found a value of 62.3 pb.

• The Verdict: This number matches the predictions from the Standard Model perfectly. It's like rolling a die a million times and getting the expected average every time. It confirms our current understanding of physics at this energy level.

Race 2: The Top Quark with a Partner (tW) at High Speed (13.6 TeV)

The Setup:
In 2022, the team ran the collider at its highest energy yet (13.6 TeV). This is the "main event" with a massive amount of data (34.7 inverse femtobarns). Here, they looked for a single top quark produced alongside a W boson (a force-carrying particle).

The Strategy:
This is harder to find because it's rarer and the background noise is louder.

• The Filter: They looked for events with two leptons (electrons or muons) of opposite charges.
• The Sorting: They categorized events by the number of jets and b-jets, focusing on three specific groups: 1 jet with 1 b-jet, 2 jets with 1 b-jet, and 2 jets with 2 b-jets.
• The Detective Work: Again, they used two separate Random Forest classifiers (digital detectives) to separate the signal from the noise. For the "2 jets, 2 b-jets" group, they looked at the energy of the second-highest energy jet to make the call.

The Result:
They measured the cross section for this process to be 82.3 pb.

• The Verdict: Just like the first race, this result agrees beautifully with the Standard Model predictions.
• Bonus: They didn't just count the total events; they also measured differential cross sections. Imagine this as not just counting how many cars passed a checkpoint, but measuring their speed, the angle they turned, and how far they traveled. They checked six different variables (like the energy of the leading lepton or the angle between particles), and in every single case, the data matched the theoretical predictions.

The Big Picture

The paper concludes with a simple message: Everything is working as expected.

• The "heavyweight" top quark behaves exactly as the Standard Model says it should.
• The measurements at 5.02 TeV are the most precise ever made by CMS at that energy.
• The measurements at 13.6 TeV are the first of their kind using data from the current "Run 3" of the LHC.

There are no signs of "new physics" (like hidden dimensions or unknown particles) in these specific measurements yet. The universe, at least in these specific top-quark interactions, is playing by the rules we already know.

Technical Summary

Technical Summary: Recent Measurements of Top-Quark Cross Sections at CMS

Problem and Motivation
The top quark, as the heaviest known fundamental particle, serves as a critical probe for precision tests of the Standard Model (SM) and a potential window into Beyond-the-SM (BSM) physics. Specifically, top-quark pair ($t\bar{t}$) production is essential for validating SM predictions, while single top quark production in association with a $W$ boson ($tW$) is sensitive to the $V_{tb}$ element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and potential BSM effects. Furthermore, the $tW$ process is notable for its quantum interference with $t\bar{t}$ production and its role as a significant background in other analyses. This contribution addresses the need for precise cross-section measurements in distinct kinematic regimes: a low-energy, low-pileup environment at 5.02 TeV and the high-energy Run 3 regime at 13.6 TeV.

Methodology
The paper presents two distinct analyses performed by the CMS Collaboration using proton-proton collision data.

1. $t\bar{t}$ Production at 5.02 TeV:

   • Dataset: 302 pb$^{-1}$ of integrated luminosity collected in 2017.
   • Selection: Events are selected using single-lepton triggers (electron or muon). The analysis requires exactly one lepton ($p_T > 20$ GeV, $|\eta| < 2.4$), at least three jets ($p_T > 25$ GeV, $|\eta| < 2.4$), and missing transverse energy ($> 30$ GeV). A veto is applied to events with a second lepton of opposite flavor with $p_T > 10$ GeV.
   • Categorization: Events are categorized into eight bins based on jet multiplicity (3 or $\ge$4 jets) and $b$-tagged jet multiplicity (1 or $\ge$2), further split by lepton flavor.
   • Background Handling: Backgrounds include single top ($t$-channel, $tW$),$W$+jets, Drell-Yan, and QCD multijets (estimated via data-driven methods). In the $3j1b$ category, where $W$+jets contamination is significant, a multivariate analysis (MVA) classifier (random forest) is trained to separate signal from background.
   • Extraction: A maximum likelihood (ML) fit is performed across all categories. Systematic uncertainties are treated as nuisance parameters. The fit utilizes the $\Delta R_{med}(j,j')$ distribution for high-purity categories ($3j2b, 4j1b, 4j2b$) and the MVA output for the $3j1b$ category.

2. $tW$ Production at 13.6 TeV:

   • Dataset: 34.7 fb$^{-1}$ of integrated luminosity from the 2022 LHC run (Run 3).
   • Selection: Events are selected using dilepton and single-lepton triggers. The selection requires at least a pair of opposite-flavor, opposite-charge leptons ($e^\pm\mu^\mp$) with the leading lepton $p_T > 25$ GeV. All leptons must satisfy $p_T > 20$ GeV and $|\eta| < 2.4$, with a minimum invariant mass of lepton pairs $> 20$ GeV.
   • Categorization: Events are classified by jet ($n$) and $b$-tagged jet ($m$) multiplicity ($n_j m_b$). Three categories are used for the inclusive measurement: $1j1b$ (highest signal purity), $2j1b$, and $2j2b$. Only the $1j1b$ category is used for differential measurements.
   • Signal Modeling: The $tW$ signal sample employs the diagram removal (DR) scheme to avoid double-counting Feynman diagrams shared with $t\bar{t}$ processes.
   • Background Handling: Backgrounds include $t\bar{t}$, Drell-Yan, diboson ($VV$),$t\bar{t}V$, and non-$W/Z$ processes. Two independent MVA classifiers (random forests) are trained for the $1j1b$ and $2j1b$ categories to discriminate signal from background. For $2j2b$, the subleading jet $p_T$ is used as the discriminant.
   • Extraction: An ML fit is performed for the inclusive cross section. Differential cross sections are obtained by unfolding detector-level results to the particle level using the TUNFOLD technique, with a veto on low-energy jets.

Key Contributions and Results

• $t\bar{t}$ Cross Section at 5.02 TeV:
  The analysis yields an inclusive cross section of $\sigma(t\bar{t}) = 62.3 \pm 1.5(\text{stat}) \pm 2.4(\text{syst}) \pm 1.2(\text{lumi})$ pb. This result is derived by combining the single-lepton channel measurement with a prior dilepton channel measurement. The value is consistent with the Standard Model prediction of $69.5^{+3.5}_{-3.7}$ pb calculated at next-to-next-to-leading order (NNLO) in perturbative QCD. The dominant uncertainties arise from integrated luminosity and $b$-tagging scale factors.

• $tW$ Cross Section at 13.6 TeV:
  This analysis presents the first single-top quark result from LHC Run 3. The inclusive cross section is measured to be $\sigma(tW) = 82.3 \pm 2.1(\text{stat}) +9.9_{-9.7}(\text{syst}) \pm 3.3(\text{lumi})$ pb. This aligns with the SM prediction of $87.9 \pm 3.1$ pb at approximate next-to-next-to-next-to-leading order (NNNLO). Leading systematic uncertainties are associated with jet energy, top quark $p_T$ modeling, and $b$-tagging efficiencies.
  Additionally, differential cross sections were measured for six variables (leading lepton $p_T$, $p_z$ of the lepton-jet system, jet $p_T$, invariant mass of the lepton-jet system, azimuthal separation $\Delta\phi$, and transverse mass). These differential distributions show good agreement with various theoretical predictions involving different matrix element generators (POWHEG, MADGRAPH5_aMC@NLO) and parton shower models (PYTHIA8, HERWIG7), utilizing both diagram removal and diagram subtraction schemes.

Significance
The paper claims that the $t\bar{t}$ measurement at 5.02 TeV represents the most precise CMS cross-section measurement for this process at that specific center-of-mass energy, leveraging the clean, low-pileup conditions of the dataset. The $tW$ measurement is significant as the first LHC single-top result utilizing Run 3 data, providing both inclusive and differential constraints on the process. All presented measurements are consistent with Standard Model predictions, reinforcing the current theoretical understanding of top-quark production mechanisms.