ATLAS EFT Results in the Top Quark Sector

This paper presents three recent ATLAS analyses using Run-2 data to systematically explore deviations from the Standard Model in the top quark sector via the Standard Model Effective Field Theory (SMEFT), demonstrating how combined measurements enhance sensitivity to Wilson coefficients and tighten constraints on new physics.

The Gist

Imagine the Standard Model of physics as a giant, incredibly detailed instruction manual for how the universe works. For decades, scientists have been checking this manual against reality, and it has been perfect. But recently, the ATLAS experiment at the Large Hadron Collider (LHC) looked for "new chapters" in the manual—particles or forces that shouldn't exist according to the current rules. They didn't find any direct evidence of these new characters.

So, instead of giving up, the scientists decided to look for faint whispers rather than loud shouts. They used a tool called an Effective Field Theory (EFT). Think of EFT like a pair of high-powered glasses. Even if you can't see a new character standing in the room, these glasses might reveal that the existing characters (like the top quark) are moving slightly differently than the manual predicts. These tiny deviations could be caused by invisible forces or particles that are too heavy to create directly, but whose "shadow" falls on the particles we can see.

This paper reports on three specific investigations using data from the ATLAS detector, where scientists smashed protons together at record speeds. They focused on the top quark, which is the heaviest particle in the Standard Model. Because it's so heavy, it's like a large ship in the ocean; even a tiny ripple from a distant, hidden storm (new physics) would cause the ship to rock noticeably.

Here are the three "detective stories" told in the paper:

1. The Top Quark and the Flash of Light ($t\bar{t}\gamma$)

The Scenario: Scientists looked at events where a pair of top quarks was created along with a photon (a particle of light).
The Analogy: Imagine two heavy dancers (the top quarks) spinning on a floor. Sometimes, they accidentally bump into a third dancer (a photon) and send it flying. The scientists measured exactly how fast and in what direction this light particle flew.
The Result: They compared the actual flight path of the light to the "perfect" path predicted by the standard manual. They found the dancers were moving exactly as the manual said they should. They also combined this data with measurements of top quarks paired with a Z boson (another heavy particle) to get an even clearer picture. The result? No hidden forces were detected; the universe is behaving exactly as expected.

2. The Solo Top Quark ($tq$)

The Scenario: This study looked at "single top quark" production, where a top quark appears on its own via a specific exchange of force (the W boson).
The Analogy: Think of this as a game of pool. Usually, you expect the balls to bounce off each other in a very specific way. The scientists were looking for a scenario where the cue ball (the top quark) seemed to be nudged by an invisible stick (a new force) that wasn't in the original rules. They used a sophisticated computer program (a neural network) to act as a referee, sorting the "good" pool shots from the "bad" ones.
The Result: After analyzing thousands of collisions, the referee found no evidence of an invisible stick. The top quarks were behaving exactly as the standard rules predicted.

3. The Shape-Shifter Search (Charged Lepton Flavour Violation)

The Scenario: This was a search for a very strange event: a top quark decaying (breaking apart) into a muon and a tau lepton at the same time.
The Analogy: In the Standard Model, particles have strict "family rules." A top quark is supposed to break apart into specific family members. It's like a parent who can only have children of a specific gender. This search looked for a "rule-breaker" event where a top quark suddenly decided to have a child that was a mix of two different families (a muon and a tau) at the same time. This is called "flavour violation."
The Result: The scientists set up a trap to catch this rule-breaking event. They looked for specific signatures in the debris of the collision. They found zero evidence of this happening. They were able to set a very strict limit: if this rule-breaking ever happens, it must be incredibly rare (less than once in a million million times).

The Big Picture

The paper concludes that after looking at 140 units of data (a massive amount of information collected over several years), the ATLAS team found no cracks in the Standard Model. The top quark is behaving exactly as the "instruction manual" says it should.

However, this isn't a failure. By proving that the top quark isn't wobbling, the scientists have tightened the screws on the theory. They have ruled out many possible "hidden chapters" that other theories might have suggested. They are essentially saying, "If new physics exists, it is hiding even deeper than we thought, or it is much weaker than we hoped."

The team is now moving forward by testing different assumptions about how strong these hidden forces might be, ensuring that as their data gets more precise, they won't miss a single whisper of the unknown.

Technical Summary

Technical Summary: ATLAS EFT Results in the Top Quark Sector

Problem Statement
With no direct evidence of Beyond the Standard Model (BSM) particle production at the TeV scale by the ATLAS experiment, deviations from Standard Model (SM) predictions must be explored systematically. The Standard Model Effective Field Theory (SMEFT) provides a framework to probe these potential BSM effects by extending the SM Lagrangian with higher-dimensional operators parameterized by Wilson coefficients. As the heaviest SM particle, the top quark is particularly sensitive to new physics, making rare top-quark processes essential probes for constraining SMEFT operators. This work addresses the need to quantify potential BSM effects and measure quantum interference between standard and effective interactions within the top quark sector using the full ATLAS Run-2 dataset.

Methodology
The analysis utilizes the complete ATLAS Run-2 dataset (2016–2018) at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $140 \text{ fb}^{-1}$. The study focuses on three distinct processes, interpreting them within the SMEFT framework using dimension-six operators defined in the Warsaw basis.

1. Theoretical Framework: The SMEFT Lagrangian is extended by higher-dimensional operators ($O^{(d)}$) scaled by a cutoff $\Lambda$. The analysis primarily considers dimension-six operators ($O^{(6)}$), though results account for both SM-EFT interference ($\Lambda^{-2}$) and EFT-EFT interference ($\Lambda^{-4}$). Monte Carlo tools such as MadGraph5_aMC@NLO and dedicated packages (SMEFTatNLO, dim6top, TopFCNC) are used to implement these operators. The new physics scale is typically fixed at $\Lambda = 1$ TeV.
2. Process 1: $t\bar{t}\gamma$ Production: Inclusive and differential cross-sections are measured in single-lepton and dilepton final states. A multi-class neural network (NN) separates signal from background in the single-lepton channel, while a binary classifier is used for the dilepton channel. The analysis extracts real and imaginary components of Wilson coefficients $C_{tB}$ and $C_{tW}$ via a profile likelihood fit to the photon transverse momentum ($p_T$) distribution.
3. Process 2: $tq$ Production ($t$-channel): Cross-sections for single top-quark production via $t$-channel exchange are measured. Events are selected based on isolated leptons, significant missing transverse energy, and exactly two high-$p_T$ jets (one $b$-tagged). An artificial NN discriminant ($D_{nn}$) is constructed to separate signal from background, with yields extracted via profile maximum-likelihood fits.
4. Process 3: Charged Lepton-Flavour Violation (cLFV): A search is conducted for cLFV interactions in $\mu\tau q t$ processes, considering both top production and decay. The selection requires two same-sign leptons, a hadronically decaying $\tau$-lepton, and at least one $b$-tagged jet.

Key Contributions and Results
The paper presents three primary analyses yielding constraints on Wilson coefficients and branching ratios:

• $t\bar{t}\gamma$ and $t\bar{t}Z$ Combination: The differential $t\bar{t}\gamma$ measurements show good agreement with the SM. A combined interpretation of $t\bar{t}\gamma$ and $t\bar{t}Z$ data provides stronger constraints, particularly on $C_{tW}$, by addressing degeneracies in limit extractions. No significant deviations from the SM are observed at the 95% confidence level (CL).
• $t$-channel Single Top: Constraints are set on two specific operators: the four-quark operator ($C^{3,1}_{Qq}/\Lambda^2$) with limits of $-0.37 < C^{3,1}_{Qq}/\Lambda^2 < 0.06$, and the operator coupling the third quark generation to the Higgs doublet ($C^3_{\phi Q}/\Lambda^2$) with limits of $-0.87 < C^3_{\phi Q}/\Lambda^2 < 1.42$.
• cLFV Search: No significant excess over the SM prediction is observed. A 95% CL limit is set on the branching ratio $B(t \to \mu\tau q) < 8.7 \times 10^{-7}$. SMEFT interpretations yield 95% CL constraints on Wilson coefficients ranging from $|C^{3(2313)}_{lequ}|/\Lambda^2 < 0.10 \text{ TeV}^{-2}$ (for $\mu\tau u t$) to $|C^{3(2323)}_{lequ}|/\Lambda^2 < 1.8 \text{ TeV}^{-2}$ (for $\mu\tau c t$).

Significance and Claims
The paper claims that the combination of improved measurements and the inclusion of new channels has significantly enhanced sensitivity to Wilson coefficients by breaking degeneracies and tightening constraints. The results demonstrate that the SMEFT framework remains a robust tool for probing the top quark sector with increasing experimental precision. Furthermore, the work highlights a shift in strategy where, given that many analyses assume $\Lambda = 1$ TeV (near the current experimental scale), the collaboration is beginning to set direct limits on $\Lambda$ itself by exploring scenarios with varying coupling strengths. These results complement previous EFT analyses and provide updated constraints on cLFV processes involving the top quark.