Measurement of the $t$-channel single top-quark production cross section at $\sqrt{s}=13$ TeV with the ATLAS detector and interpretations of the measurement

The ATLAS collaboration measured the $t$-channel single top-quark production cross sections in proton-proton collisions at $\sqrt{s}=13$ TeV, obtaining precise values for top-quark and top-antiquark rates that were subsequently used to set limits on EFT operators and CKM matrix elements.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed particle racetrack where protons (tiny subatomic particles) are smashed together at nearly the speed of light. When these crashes happen, they create a shower of new particles. Most of the time, these particles are common and predictable, like standard traffic on a highway. But occasionally, something rare and special happens: a "top quark" is created.

The top quark is the heaviest of all known elementary particles. It's like the "sumo wrestler" of the particle world. Because it's so heavy, it's hard to make, and it disappears almost instantly. This paper is about a specific way the ATLAS detector (a massive camera and computer system surrounding the racetrack) catches these rare top quarks.

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

1. The "T-Channel" Delivery Method

There are a few different ways top quarks can be born in these collisions. The most common way is called the "t-channel."

Think of the Standard Model (the rulebook of physics) as a busy post office. Usually, packages (particles) are delivered via standard routes. But in the t-channel, a top quark is delivered via a very specific, slightly unusual shortcut involving a "virtual W boson" (a messenger particle). It's like a courier taking a secret back-alley route to drop off a heavy package. The scientists wanted to count exactly how many of these specific deliveries happen.

2. The Great Filter (Finding the Needle in the Haystack)

The problem is that for every one of these rare top quark deliveries, there are millions of other "junk" collisions happening at the same time. It's like trying to find a specific, rare coin in a pile of a million regular coins.

To solve this, the ATLAS team built a digital sieve using a "Neural Network" (a type of computer brain).

• The Setup: They looked for collisions that had exactly one electron or muon (a type of light particle), a lot of missing energy (like a ghost that slipped away), and exactly two jets of debris.
• The Filter: One of those jets had to be tagged as coming from a "bottom quark" (a specific type of heavy particle).
• The Score: The computer brain gave every collision a score. If the score was high, it was likely a top quark. If it was low, it was just background noise.

3. The Count

After running their sieve on data collected over four years (2015–2018), they counted the results:

• Top Quarks (the "matter" version): They found about 137 of these per unit of measurement.
• Top Antiquarks (the "anti-matter" version): They found about 84.
• The Ratio: Interestingly, they found about 1.6 times more top quarks than top antiquarks.

This ratio is important because it acts like a fingerprint. Different theories about how the universe is built (specifically, how the "parton distribution functions" or PDFs work—think of these as maps of how the proton is packed inside) predict different ratios. The ATLAS result matched the best current maps almost perfectly.

4. Checking the Rulebook (Interpretations)

The scientists didn't just stop at counting; they asked, "Does this match the rulebook, or is there a new rule we need to write?"

Test A: The "Contact Interaction" (EFT)
They checked if there was a hidden, four-way handshake between particles that shouldn't exist. They looked for a specific "Wilson coefficient" (a number that measures the strength of this handshake).

• The Result: The number they found was essentially zero (between -0.37 and 0.06). This means the "handshake" doesn't exist, and the Standard Model rulebook remains unbroken.

Test B: The "Mixing Cards" (CKM Matrix)
In the Standard Model, particles have a "preference" for which other particles they turn into. This is described by a set of numbers called the CKM matrix (imagine a deck of cards where the top quark prefers to turn into a bottom quark, but has a tiny, tiny chance of turning into a down or strange quark).

• The Result: They measured these preferences and found they matched the Standard Model's predictions exactly. The top quark is behaving exactly as the rulebook says it should.

The Bottom Line

The ATLAS collaboration took a massive amount of data, filtered out the noise, and counted the rarest of rare particles. They found that:

1. The number of top quarks produced matches the Standard Model predictions perfectly.
2. The ratio of top quarks to anti-top quarks is exactly what we expect.
3. There is no evidence of "new physics" or hidden forces messing with these particles yet.

In short, the universe is behaving exactly as the current rulebook says it should, at least when it comes to this specific type of top quark delivery. The "secret back-alley route" is well understood, and no new shortcuts have been discovered.

Technical Summary

Technical Summary: Measurement of the t-channel Single Top-Quark Production Cross Section at $\sqrt{s} = 13$ TeV

Problem and Motivation
The t-channel exchange of a virtual $W$ boson represents the dominant production mechanism for single top-quarks at the Large Hadron Collider (LHC). Precise measurement of this process serves two primary physics goals: testing the predictions of the Standard Model (SM) and probing for potential contributions from physics beyond the SM (BSM). Specifically, the ratio of production cross sections for top-quarks to top-antiquarks ($R_t = \sigma_{tq}/\sigma_{\bar{t}q}$) offers sensitivity to Parton Distribution Function (PDF) predictions, while the total cross section provides constraints on Effective Field Theory (EFT) operators, such as $O_{Qq}^{3,1}$. This work presents the latest measurement of the t-channel production cross section by the ATLAS Collaboration using the full Run 2 dataset (2015–2018).

Methodology
The analysis utilizes proton-proton collision data at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$. Event selection targets the leading-order t-channel signature, requiring:

• Exactly one charged light lepton (electron or muon).
• High missing transverse energy.
• Exactly two jets, with exactly one jet identified as a $b$-jet using the DL1r tagger at a 60% working point.

To distinguish signal events from background processes (including $t\bar{t}$, $W$+jets, and diboson production), a feed-forward Neural Network (NN) is trained on 17 input variables. The analysis defines two separate signal regions based on the electric charge of the lepton. Cross sections are extracted by performing a binned maximum likelihood fit to the NN output score distribution ($D_{nn}$).

Key Contributions and Results
The primary contribution of this work is the precise determination of the t-channel single top-quark production cross sections:

• Single top-quark production: $\sigma_{tq} = 137^{+8}_{-8}$ pb.
• Single top-antiquark production: $\sigma_{\bar{t}q} = 84^{+6}_{-5}$ pb.
• Combined cross section: $\sigma_{tq+\bar{t}q} = 221^{+13}_{-13}$ pb.
• Cross section ratio: $R_t = 1.636^{+0.036}_{-0.034}$.

The measured $R_t$ value is compared against Next-to-Next-to-Leading Order (NNLO) theoretical predictions calculated with MCFM using various PDF sets. The results show good agreement with most predictions within uncertainties.

Interpretations
The paper provides two specific interpretations of the measurement:

1. EFT Constraints: Limits are set on the Wilson coefficient of the four-fermion contact interaction operator $O_{Qq}^{3,1}$, which involves third-generation quarks and first/second-generation quarks. This operator modifies the top-quark production angle and fiducial acceptance. A likelihood scan yields a 95% confidence interval of $-0.37 \leq C_{Qq}^{3,1}/\Lambda^2 \leq 0.06$, consistent with the Standard Model.
2. CKM Matrix Elements: Constraints are placed on the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|$, $|V_{ts}|$, and $|V_{tb}|$. By modeling the production and decay of single top quarks via $Wtq$ vertices and performing two-dimensional likelihood scans, the analysis constrains the parameters $f_{LV} \cdot |V_{tq}|$. The results are compatible with SM expectations.

Significance
This measurement provides the most precise results for the t-channel single top-quark production process to date. The agreement between the experimental data and NNLO theory predictions reinforces the validity of the Standard Model in this sector. Furthermore, the derived constraints on the EFT operator $O_{Qq}^{3,1}$ and the CKM matrix elements demonstrate the utility of single top-quark production as a probe for new physics and precision flavor physics. All interpretations presented yield results compatible with the Standard Model.