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Search for physics beyond the standard model in four and three top quark production events using proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb⁻¹ of proton-proton collision data at 13 TeV collected by the CMS detector, this study searches for physics beyond the Standard Model in four- and three-top quark production events to constrain effective field theory Wilson coefficients, exclude narrow topphilic heavy resonances, and extract the top quark Yukawa coupling.

Original authors: CMS Collaboration

Published 2026-07-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "particle blender." Scientists smash protons together at nearly the speed of light to see what tiny fragments fly out. Usually, they look for common particles, but sometimes, they look for the "rare gems"—events where four heavy top quarks (the heaviest known elementary particles) are created at once, or three top quarks plus something else.

This paper is a report from the CMS Collaboration, a team of scientists using a giant detector called CMS to catch these rare events. They analyzed data from 2016 to 2018, which is like looking at a library containing 138 billion "pages" of collision data.

Here is what they did and found, broken down into simple concepts:

1. The Hunt for the "Four-Top" and "Three-Top" Party

Top quarks are like the "heavyweights" of the particle world. They are so heavy and unstable that they decay (fall apart) almost instantly. To find them, scientists look for their "debris," which often includes electrons and muons (lighter cousins of electrons).

The team specifically looked for events where the debris included:

Two electrons/muons with the same electric charge (like two positive magnets repelling each other).
Three or four electrons/muons.

These specific combinations are very rare in the "Standard Model" (our current rulebook of physics). Because they are rare, they are perfect places to look for "new physics"—rules that we haven't discovered yet.

2. The Three Ways They Looked for New Physics

The scientists didn't just look for a specific new particle; they looked for any deviation from the rulebook using three different "lenses" or theories:

Lens A: The "Rulebook Tweaks" (SMEFT)
Imagine the Standard Model is a recipe book. The scientists asked: "What if we slightly tweak the ingredients?" They used a framework called SMEFT (Standard Model Effective Field Theory) to test six specific "tweaks" (mathematical adjustments) that could change how top quarks interact with each other or with the Higgs boson (the particle that gives others mass).

The Analogy: It's like checking if a cake rises differently because someone secretly added a pinch of salt or sugar.
The Result: They didn't find any secret ingredients. The data matched the original recipe perfectly.

Lens B: The "Heavy Resonance" Search
They looked for "heavy resonances." Imagine a heavy, invisible drum that, when hit, breaks apart into top quarks.

The Analogy: If you hear a specific drumbeat, you know a specific drum was hit. The scientists looked for a "drumbeat" (a spike in data) that would indicate a new, heavy particle decaying into top quarks. They checked for different types of "drums" (scalar, pseudoscalar, and vector particles) and different colors (how they interact with the strong nuclear force).
The Result: They didn't hear any new drumbeats. They ruled out the existence of these heavy particles in a mass range between 400 GeV and 1.6 TeV (roughly 400 to 1,600 times the mass of a proton).

Lens C: The "Top-Higgs Connection"
The top quark and the Higgs boson have a special relationship called the "Yukawa coupling." Think of it as the strength of a handshake between them.

The Analogy: Is the handshake firm (standard), weak, or is it a "ghostly" handshake that only happens in a mirror (a property called CP-odd)?
The Result: They measured the handshake strength. It was consistent with the Standard Model, though with a little wiggle room. They confirmed that the "ghostly" handshake isn't the only thing happening, but they couldn't rule out a slightly stronger or weaker handshake entirely.

3. The "Fingerprint" Problem

One of the interesting challenges in this paper is that the "debris" from a four-top event looks almost identical to the debris from a three-top event.

The Analogy: Imagine trying to tell the difference between a car crash involving four cars and one involving three cars, but you can only see the scattered glass and a few tires. It's very hard to tell which scenario happened just by looking at the mess.
The Solution: The scientists used a sophisticated computer program (a machine learning algorithm) to act like a super-detective. It analyzed the patterns of the debris to guess which scenario was more likely. They found that the data contained a mix of both, and they couldn't perfectly separate them, so they treated them as a combined signal.

4. The Final Verdict

After analyzing all the data, the scientists found:

A Slight Excess: They saw a tiny bit more "four-top" and "three-top" events than the Standard Model predicted (about 1.3 standard deviations higher). However, this is not enough to claim a discovery; it's like hearing a faint rustle in the bushes that could be a cat or just the wind.
No New Physics Found: In all three "lenses" they used, the data was statistically compatible with the Standard Model. They did not find evidence of new heavy particles, new rules for how quarks interact, or a strange new type of handshake between the top quark and the Higgs boson.

Summary

The CMS team took a massive snapshot of the universe's most energetic collisions, looking for the rarest of rare events (four top quarks at once). They used three different theoretical tools to search for cracks in our current understanding of physics. While they found a tiny, unexplained "glitch" in the data, it wasn't significant enough to rewrite the rulebook. For now, the Standard Model remains the champion, and the search for "new physics" in this specific area continues.

Technical Summary: Search for BSM Physics in Four and Three Top Quark Production

Problem and Motivation
The top quark, as the heaviest elementary particle in the Standard Model (SM), plays a critical role in understanding electroweak symmetry breaking. Rare production processes involving multiple top quarks, specifically the simultaneous production of four top quarks ($tttt$) and three top quarks in association with a $W$ boson or a light quark ($tttW$, $tttq$, collectively $ttt$), serve as sensitive probes for physics beyond the Standard Model (BSM). These processes are predicted to be enhanced in various BSM scenarios, including supersymmetry, compositeness, extra dimensions, extended Higgs sectors, and models involving dark matter or axion-like particles. Furthermore, modifications to the top quark Yukawa coupling and the presence of heavy resonances decaying to top quarks can significantly alter the cross sections and kinematic distributions of these rare events. While previous analyses by the ATLAS and CMS collaborations have observed $tttt$ production, this paper aims to provide a comprehensive interpretation of the $tttt$ and $ttt$ data within three specific BSM frameworks: the Standard Model Effective Field Theory (SMEFT), searches for narrow topphilic heavy resonances, and the extraction of the top quark Yukawa coupling's CP structure.

Methodology
The analysis utilizes proton-proton collision data recorded by the CMS detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV during the 2016–2018 run, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$ .

Event Selection: Events are selected requiring exactly two same-sign, three, or four tight leptons (electrons or muons), no additional loose leptons, and at least two jets with at least one $b$ -tagged jet. The selection is categorized into exclusive signal regions (SRs) and control regions (CRs) based on the number of jets ( $N_j$ ), $b$ -jets ( $N_b$ ), the scalar sum of jet transverse momenta ( $H_T$ ), and the presence of $Z$ boson candidates.
Signal and Background Modeling: The $tttt$ signal is simulated at next-to-leading order (NLO) in QCD, while $ttt$ production is simulated at NLO using a diagram removal scheme to avoid overlap with $tttt$. Backgrounds, including $ttZ$, $ttW$, $ttH$, and non-prompt lepton sources, are estimated using a combination of simulation and data-driven methods (e.g., the "tight-to-loose" ratio method).
Discrimination: Multiclassification Boosted Decision Trees (BDTs) are employed to distinguish between the $tttt$ signal, associated top production ($ttX$), and $t\bar{t}$ backgrounds.
Fit Strategy: Likelihood fits are performed on the BDT score distributions or the $H_T$ distribution, depending on the specific BSM scenario being tested. The $H_T$ distribution is utilized for SMEFT and resonance searches due to its sensitivity to high-energy enhancements, while the BDT score is used for the SM cross-section measurement and Yukawa coupling extraction. Systematic uncertainties, including those related to luminosity, detector performance, and theoretical modeling (scale variations, PDFs), are incorporated as nuisance parameters.

Key Contributions
This work presents the first simultaneous interpretation of $tttt$ and $ttt$ production data within a single analysis framework for three distinct BSM scenarios:

SMEFT Interpretation: Constraints are derived on six dimension-6 Wilson coefficients ( $c_{tt}$ , $c^{(1)}_{QQ}$ , $c^{(1)}_{Qt}$ , $c^{(8)}_{Qt}$ , $c^{\text{Re}}_{tH}$ , and $c^{\text{Im}}_{tH}$ ) that modify four-heavy-quark and top-Higgs interactions. This is the first analysis optimized for $tttt$ production to consider these six operators simultaneously.
Heavy Resonance Search: Exclusion limits are set on six simplified models of narrow topphilic heavy resonances (scalar, pseudoscalar, and vector bosons in color-singlet and color-octet states) with masses ranging from 400 GeV to 1.6 TeV.
Yukawa Coupling Extraction: The top quark Yukawa coupling is extracted, parameterizing both CP-even ( $\kappa_t$ ) and CP-odd ( $\tilde{\kappa}_t$ ) contributions, utilizing a parameterization that includes quartic terms to capture effects beyond the linear SMEFT approximation.

Results

SM Cross Section: The measured $tttt$ production cross section is $\sigma(tttt) = 18.9^{+4.4}_{-4.0}$ fb, which is consistent with the SM prediction of $13.4^{+1.0}_{-1.8}$ fb within approximately 1.3 standard deviations. A strong anticorrelation ( $\rho = -0.98$ ) is observed between the $tttt$ and $ttt$ cross sections, confirming that the experimental analysis cannot distinguish between the two processes in the most sensitive regions.
SMEFT Constraints: The data are statistically compatible with the SM expectation (zero Wilson coefficients). The analysis provides the first constraints on the imaginary part of the top-Higgs Wilson coefficient ( $c^{\text{Im}}_{tH}$ ) from a $tttt$ production analysis. The observed exclusion intervals for four-heavy-quark operators are 12–25% tighter than previous CMS multilepton EFT measurements and 64–89% tighter than ATLAS $tttt$ cross-section measurements.
Resonance Exclusions: No significant excess is observed. Exclusion limits are set on the coupling strength of topphilic resonances as a function of mass. For color-octet models, physical scenarios are excluded for masses below 1.4–1.6 TeV. For color-singlet models, limits are generally weaker, with physical exclusions only for masses below 600–800 GeV.
Yukawa Coupling: The extracted Yukawa coupling modifiers are consistent with the SM expectation ( $\kappa_t = 1, \tilde{\kappa}_t = 0$ ) at the one-standard-deviation level. The observed 95% confidence level interval for $|\kappa_t|$ (with $\tilde{\kappa}_t=0$ fixed) is $0.7 < |\kappa_t| < 1.4$ , which is significantly tighter than previous constraints derived solely from $tttt$ production.

Significance
The paper claims significance primarily through the simultaneous treatment of $tttt$ and $ttt$ production as signal processes, acknowledging their indistinguishability in current experimental signatures and their similar modification patterns under BSM scenarios. By employing optimized observables ( $H_T$ for high-energy sensitivity and BDT scores for purity) and a unified fit framework, the analysis achieves improved constraints on SMEFT operators compared to previous individual measurements. The work provides the first simultaneous constraints on six specific Wilson coefficients in a $tttt$-optimized analysis and offers the most stringent limits to date on the top quark Yukawa coupling derived from multi-top production, while also establishing exclusion limits on a broad range of topphilic heavy resonance models. The results are statistically compatible with the Standard Model, reinforcing the current understanding of top quark physics while setting precise boundaries for potential new physics.

1. The Hunt for the "Four-Top" and "Three-Top" Party

2. The Three Ways They Looked for New Physics

3. The "Fingerprint" Problem

4. The Final Verdict

Summary

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