Measurement of the $t$-channel single top quark cross section in proton-proton collisions at $\sqrt{s}$ = 5.02 TeV

This paper presents the first CMS measurement of the $t$-channel single top quark production cross section in proton-proton collisions at $\sqrt{s} = 5.02$ TeV, utilizing 302 pb$^{-1}$ of 2017 data to report combined and individual cross sections for top quarks and antiquarks that are consistent with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. Usually, it runs at a blistering speed, smashing protons together with the energy of a speeding train. But in 2017, the scientists decided to run a "special low-speed run," smashing particles at a more modest energy level (5.02 TeV).

Why? Think of it like a chef testing a new recipe. You don't just cook at high heat; you test at medium heat to see if the ingredients behave differently. This paper is the report card on what happened when the CMS detector (a giant, high-tech camera) took pictures of these specific collisions.

Here is the story of what they found, explained simply:

1. The Main Character: The Top Quark

The star of this show is the top quark. It's the heaviest fundamental particle we know, like the "sumo wrestler" of the particle world. Because it's so heavy, it's incredibly unstable. It lives for a split second (about $10^{-25}$ seconds) before it bursts apart. It's so fast that it doesn't have time to get dressed in a "costume" (form a bound state with other particles) before it dies. This makes it a unique, naked particle that scientists can study directly.

2. The Process: The "T-Channel" Dance

Usually, top quarks are made in pairs (like a dance couple). But sometimes, they are made alone. This paper focuses on a specific way they are made alone, called the "t-channel."

• The Analogy: Imagine two billiard balls (protons) colliding. Inside one ball, there's a "bottom quark" (a heavy particle). It swaps a "W boson" (a force carrier, like a messenger) with a particle from the other ball.
• The Result: This exchange knocks a top quark out of the mix, and a "light quark" (a lighter particle) gets kicked backward.
• Why it matters: This process is sensitive to the "bottom quark" inside the proton. It's like trying to figure out what's inside a wrapped gift by watching how the wrapping paper tears when you throw it against a wall.

3. The Investigation: Finding the Needle in the Haystack

The scientists had 302 "picobarns" of data (a unit of how many collisions they watched). They were looking for a very specific signature:

• The Clues: One electron or muon (a heavy cousin of an electron), a missing piece of energy (a neutrino that escaped the detector), and several jets of debris (particles flying out).
• The Filter: They had to filter out the "noise." Most collisions just create a mess of junk (QCD multijets) or pairs of top quarks. The team used advanced computer filters (called Machine Learning or MVA) to separate the "single top" signal from the background noise, much like a bouncer at a club checking IDs to let only the right people in.

4. The Results: The Scorecard

After all the filtering and math, they measured how often this "single top" event happened.

• The Count: They found that for every trillion collisions, this specific event happened about 25.4 times (measured in picobarns).
• The Breakdown: They also counted how many were "top quarks" (matter) vs. "top antiquarks" (antimatter). They found about 17.6 matter tops and 6.6 antimatter tops.
• The Ratio: The ratio of matter to antimatter was about 2.7 to 1. This is a crucial number because it tells us about the internal structure of the proton.

5. The Big Question: Is the Standard Model Right?

The "Standard Model" is the rulebook of physics. It predicts exactly how often these events should happen.

• The Verdict: The scientists compared their measurements (25.4) with the rulebook's prediction (around 30.3).
• The Outcome: The numbers are close enough to say, "Yes, the rulebook is still correct!" The measurements agree with the Standard Model predictions within the margin of error.

6. The Secret Ingredient: The CKM Matrix

The paper also calculated a value called $|V_{tb}|$.

• The Analogy: Think of the Standard Model as a family tree of quarks. $|V_{tb}|$ measures how strongly the top quark is related to the bottom quark. The theory says this relationship should be 1.0 (they are best friends).
• The Finding: The experiment measured it to be 0.92. This is very close to 1.0, confirming that the top quark almost exclusively decays into a bottom quark, just as the theory predicts.

Summary

In plain English:
The CMS team took a "low-energy" snapshot of the universe in 2017. They looked for a rare event where a heavy top quark is created alone. They found it, counted it, and checked the numbers against the laws of physics. Everything matched up. The universe is behaving exactly as we thought it would, even at this specific energy level. This gives scientists more confidence that our current understanding of the subatomic world is solid, even as they look for the tiny cracks where "New Physics" might be hiding.

Technical Summary

1. Problem and Motivation

The top quark, being the heaviest fundamental particle, decays before hadronizing, allowing it to be studied as an asymptotically free particle. Single top quark production via the t-channel is a dominant process at the Large Hadron Collider (LHC) and is sensitive to the bottom quark parton distribution function (PDF) and the Cabibbo–Kobayashi–Maskawa (CKM) matrix element $|V_{tb}|$.

While the ATLAS and CMS collaborations have previously measured this process at $\sqrt{s} = 7, 8,$ and $13$ TeV, and ATLAS recently reported a measurement at $5.02$ TeV, this paper presents the first CMS measurement of the t-channel single top quark cross section at this specific energy.

• Scientific Goal: To test the Standard Model (SM) predictions at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD) across different energy scales.
• Specific Context: The data comes from a special low-energy, low-intensity LHC run in 2017. A key feature of this dataset is the extremely low pileup (average number of interactions per bunch crossing $\approx 2$) compared to standard 13 TeV runs ($\approx 32$), offering a cleaner detector environment for reconstruction.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collision data collected by the CMS detector in 2017 at $\sqrt{s} = 5.02$ TeV, corresponding to an integrated luminosity of 302 pb$^{-1}$.
• Signal Process: t-channel single top quark ($tq$) and single top antiquark ($\bar{t}q$) production.
• Background Processes:
  • Top quark pair ($t\bar{t}$) production.
  • Single top in s-channel and associated $tW$ production.
  • $W$+jets and Drell-Yan (DY)+jets.
  • QCD multijet events (estimated via data-driven methods).
• Simulation: Signal and most backgrounds were simulated using POWHEG (v2) interfaced with PYTHIA 8 (CP5 tune) for parton showering. Cross-section normalizations were based on NNLO QCD calculations (using MCFM, TOP++, etc.).

Event Selection

The analysis targets the leptonic decay of the top quark ($t \to Wb \to \ell\nu b$, where $\ell = e, \mu$).

• Trigger: Events required at least one electron ($p_T > 20$ GeV) or muon ($p_T > 17$ GeV).
• Object Reconstruction:
  • Leptons: Identified with strict isolation and impact parameter requirements.
  • Jets: Clustered using the anti-$k_T$ algorithm ($R=0.4$).
  • b-tagging: The DEEPCSV algorithm (medium working point) was used to identify jets from $b$-quark fragmentation.
• Kinematic Cuts:
  • Exactly one lepton.
  • Missing transverse momentum ($p_T^{miss}$) $> 30$ GeV.
  • Transverse mass of the lepton-$p_T^{miss}$ system ($m_T^W$) $> 50$ GeV.
  • Scalar sum of $p_T$ ($H'_T$) $> 170$ GeV.
• Event Categories: Events were classified into 12 mutually exclusive categories based on:
  • Lepton charge ($+$ or $-$).
  • Lepton flavor ($e$ or $\mu$).
  • Jet multiplicity: 2j1b (2 jets, 1 b-tagged), 3j1b (3 jets, 1 b-tagged), and 3j2b (3 jets, 2 b-tagged). The 2j1b category contains the majority of signal events.

Analysis Strategy

• Top Reconstruction: The neutrino's longitudinal momentum ($p_z^\nu$) was inferred by constraining the $W$ boson mass to its known value. The top quark was reconstructed from the lepton, neutrino, and b-jet.
• Multivariate Analysis (MVA):
  • For the 2j1b categories (dominated by $W$+jets background), a Random Forest classifier was trained to distinguish signal from background using variables like the pseudorapidity of the untagged jet ($|\eta_{u0}|$), transverse mass, and invariant masses.
  • For 3j1b and 3j2b categories (dominated by $t\bar{t}$ background), the absolute pseudorapidity of the leading untagged jet ($|\eta_{u0}|$) was used as the sole discriminant, leveraging the forward nature of the t-channel recoil jet.
• Statistical Extraction: Cross sections were extracted using binned maximum likelihood (ML) fits to the MVA score (for 2j1b) and $|\eta_{u0}|$ (for others) distributions. The fit included signal strength modifiers ($r$) for $tq$ and $\bar{t}q$ and constrained nuisance parameters for systematic uncertainties.

3. Key Contributions

1. First CMS Measurement at 5.02 TeV: Provides a crucial data point for testing the energy dependence of t-channel single top production, complementing the ATLAS measurement at the same energy.
2. Low-Pileup Advantage: Demonstrates the capability of the CMS detector to perform precision measurements in low-pileup conditions, which reduces reconstruction ambiguities and improves jet/lepton resolution.
3. Differential Constraints: By measuring the ratio of top to antiquark cross sections ($R_{t-ch}$), the analysis provides constraints on the $b$-quark PDF and the CKM matrix element $|V_{tb}|$.
4. Comprehensive Uncertainty Treatment: Utilizes the Barlow-Beeston "light" method for statistical uncertainties from MC samples and treats systematic uncertainties (detector, background, theory) as nuisance parameters in a global fit.

4. Results

The measured cross sections are in good agreement with SM predictions:

• Combined Cross Section ($tq + \bar{t}q$):
  $$\sigma(tq + \bar{t}q) = 25.4 \pm 3.5 (\text{stat}) \pm 3.9 (\text{syst}) \pm 0.5 (\text{lumi}) \text{ pb}$$
  (Total relative uncertainty $\approx 21\%$)

• Individual Cross Sections:

  • Top quark ($tq$):$\sigma(tq) = 17.6 \pm 2.7 (\text{stat}) \pm 2.4 (\text{syst}) \pm 0.3 (\text{lumi}) \text{ pb}$
  • Top antiquark ($\bar{t}q$): $\sigma(\bar{t}q) = 6.6 \pm 1.6 (\text{stat}) \pm 2.5 (\text{syst}) \pm 0.1 (\text{lumi}) \text{ pb}$

• Cross Section Ratio:
  $$R_{t-ch} = \frac{\sigma(tq)}{\sigma(\bar{t}q)} = 2.7 \pm 0.8 (\text{stat}) \pm 0.3 (\text{syst})$$

• CKM Matrix Element:
  Assuming the top decays only to $Wb$ and $|V_{td}|, |V_{ts}| \ll |V_{tb}|$, the absolute value of the CKM element is measured as:
  $$|f_{LV} V_{tb}| = 0.92 \pm 0.09 (\text{exp}) \pm 0.01 (\text{theo})$$
  (Consistent with the SM expectation of $|V_{tb}| \approx 1$)

• Dominant Uncertainties: The measurement is primarily limited by uncertainties in b-tagging scale factors and the normalization of $W$+c jets.

5. Significance

• Standard Model Validation: The results confirm the NNLO QCD predictions for t-channel single top production at $\sqrt{s} = 5.02$ TeV, reinforcing the consistency of the Standard Model across different energy regimes.
• PDF Constraints: The measurement of the $tq/\bar{t}q$ ratio provides valuable input for refining the $b$-quark parton distribution function within the proton, particularly in the momentum fraction region probed at this energy.
• Future Prospects: This analysis validates the methodology for using low-pileup datasets for precision physics, which is relevant for future LHC runs and potential future colliders where pileup conditions may vary. The consistency with the ATLAS measurement at the same energy strengthens the global understanding of single top production.