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Search for pair-produced vector-like top quarks decaying into Lorentz-boosted top quarks and scalar bosons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this paper presents a search for pair-produced vector-like top quarks decaying into a scalar boson and a standard model top quark, finding no significant evidence for new physics and setting 95% confidence level upper limits on the production cross section.

Original authors: CMS Collaboration

Published 2026-10-05

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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

For decades, physicists have relied on a framework called the Standard Model to explain how the universe works at its most fundamental level. It successfully describes the particles that make up matter and the forces that hold them together, including the discovery of the Higgs boson, a particle that gives other particles their mass. Yet, this framework is incomplete. It leaves a major puzzle unsolved regarding the mass of the Higgs boson itself. According to the math, quantum effects should make this particle incredibly heavy, but observations show it is relatively light. This discrepancy, known as the hierarchy problem, suggests that there must be new physics hiding just beyond our current view, perhaps in the form of heavy, unseen partners to the particles we already know.

One popular idea to solve this puzzle involves "vector-like quarks," hypothetical heavy cousins of the top quark, the heaviest known particle. In some theories, these new particles would interact with the Higgs field in a way that cancels out the problematic quantum corrections, stabilizing the universe's structure. If these heavy partners exist, they would likely be produced in pairs during high-energy collisions and then decay into a standard top quark and a new, lighter particle, often a type of scalar boson. Finding these heavy partners would not only solve a deep theoretical mystery but also open a window into a richer, more complex version of reality than the one we currently see.

A researcher using the CMS detector at the Large Hadron Collider in Switzerland has conducted a massive search for these elusive particles. They analyzed data corresponding to an integrated luminosity of 138 fb⁻¹, collected from proton-proton collisions over three years of operation at the world's most powerful particle accelerator. The scientist was looking for a very specific signature: a pair of heavy vector-like top quarks decaying into two standard top quarks and two new scalar bosons. The challenge was that these events are rare and buried under a mountain of ordinary background noise. To find them, they focused on a scenario where one of the new scalar bosons breaks apart into two high-energy photons, while the two standard top quarks smash into the detector as single, massive clumps of debris known as large-radius jets.

The researcher built a sophisticated strategy to separate the signal from the noise. They used advanced computer algorithms to identify the massive jets created by the speeding top quarks and to distinguish the clean, sharp signals of the two photons from other particles that might mimic them. Because the theoretical predictions for the background noise in this specific channel are difficult to calculate with perfect precision, they used a clever data-driven approach. They defined a "control region" where the events failed the strict photon identification criteria, allowing them to measure the background behavior directly from the data itself. They then used a mathematical relationship to predict what that background should look like in the "signal region," where the photons passed all the tests. This method allowed them to rely on the actual data rather than just computer simulations to understand what they were seeing.

After sifting through the data, the researcher found no evidence of the heavy vector-like top quarks they were hunting. The number of events they observed matched the predictions for the background noise almost perfectly. There was one small fluctuation in the data that looked slightly unusual, appearing with a statistical significance of 2.7 standard deviations. In the world of particle physics, this is a hint, but not a discovery; it is the kind of statistical wobble that happens by chance roughly once in every few hundred trials. When they accounted for the fact that they had looked at many different possible mass combinations, this hint faded further, dropping to a significance of just 1.5 standard deviations, which is consistent with random noise.

Consequently, the study did not find the new particles, but it did achieve something important by ruling them out within a specific range. The researcher set strict upper limits on how often these heavy particles could be produced, effectively telling us that if they exist, they must be heavier than the masses they tested or they interact with the rest of the universe in a way that makes them even harder to find. They probed masses for the vector-like top quark ranging from 800 to 1,800 billion electron volts and for the new scalar boson from 100 to 300 billion electron volts. While the search came up empty, it represents the first time scientists have looked for this specific type of heavy particle decay in this high-energy, "boosted" regime. The absence of a discovery narrows the path for future theories, forcing physicists to refine their models or look for these heavy partners at even higher energies in the years to come.

Technical Summary: Search for Pair-Produced Vector-Like Top Quarks Decaying into Lorentz-Boosted Top Quarks and Scalar Bosons

Problem and Motivation
The Standard Model (SM) successfully describes particle physics but lacks a mechanism to stabilize the Higgs boson mass against quadratic quantum corrections at large mass scales, a theoretical issue known as the hierarchy problem. Vector-like quarks (VLQs) are hypothetical heavy partners of SM quarks proposed in various Beyond the Standard Model (BSM) scenarios, including composite Higgs models, to resolve this hierarchy problem by offsetting top-quark loop corrections. While previous searches have constrained VLQs decaying via standard channels ( $T \to Zt, Ht, Wb$ ), this paper addresses a specific topology predicted by composite Higgs models: the pair production of vector-like top quarks ( $T\bar{T}$ ) where each $T$ decays into a SM top quark and a new neutral scalar boson ( $\phi$ ). In this scenario, the scalar boson subsequently decays into a diphoton pair ( $\phi \to \gamma\gamma$ ). This specific decay chain ( $T\bar{T} \to t\bar{t}\phi\phi \to t\bar{t}\gamma\gamma + \text{invisible/undetected}$ ) had not been exclusively searched for in the boosted regime prior to this analysis.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The search targets events characterized by:

Boosted Top Quarks: Due to the high mass of the $T$ quark (considered in the range 800–1800 GeV), the resulting top quarks are highly Lorentz-boosted. Their decay products are reconstructed as single large-radius jets (AK8 jets) with a distance parameter of 0.8.
Diphoton Signature: One of the two scalar bosons ( $\phi$ ) is required to decay into two photons. The other $\phi$ is treated as detector-stable in the simulation for the purpose of signal acceptance, with a correction factor applied to account for the physical decay of both bosons.
Event Selection: Events are selected requiring at least two AK8 jets with transverse momentum ( $p_T$ ) > 350 GeV and a groomed jet mass ( $m_{SD}$ ) > 50 GeV. These jets must pass a top-quark tagging requirement using the ParticleNet algorithm (working point with 0.5% misidentification rate for light jets). Additionally, at least two photons with $p_T > 25$ GeV are required.
Background Estimation: The dominant SM background consists of top-quark pair production ( $t\bar{t}$ ) with misidentified or non-prompt photons. Because simulating these backgrounds reliably is difficult, the analysis employs a data-driven approach. A Control Region (CR) is defined where photon candidates fail the identification criteria, while the Signal Region (SR) requires passing candidates. A transfer function (TF), parameterized as an exponential decay dependent on the reconstructed scalar mass ( $m_{\phi}^{\text{reco}}$ ), is derived to extrapolate the $t\bar{t}$ background from the CR to the SR. A simultaneous maximum-likelihood fit is performed in the two-dimensional plane of reconstructed $T$ mass ( $m_T^{\text{reco}}$ ) and $m_{\phi}^{\text{reco}}$ .
Statistical Analysis: The signal strength parameter is extracted using the $CL_s$ method. Systematic uncertainties, including those from jet energy scale, pileup, and luminosity, are incorporated as nuisance parameters.

Key Contributions

First Exclusive Boosted Search: This work presents the first exclusive search for pair-produced vector-like top quarks in the boosted regime decaying via the $T \to \phi t$ channel with $\phi \to \gamma\gamma$ .
Advanced Tagging: The analysis utilizes the ParticleNet deep learning algorithm to identify large-radius jets originating from hadronic decays of Lorentz-boosted top quarks, achieving high efficiency while suppressing light-quark and gluon backgrounds.
Data-Driven Background Modeling: The paper demonstrates a robust method for estimating the challenging $t\bar{t} + \text{photons}$ background using a transfer function derived from data in a control region, validated in a separate validation region (VR).
Comprehensive Mass Scan: The search covers a grid of 55 mass combinations, scanning $m_\phi$ from 100 to 300 GeV and $m_T$ from 800 to 1800 GeV.

Results
The analysis observed no significant deviation from the predicted background across the scanned mass grid.

Significance: The largest local excess was observed for the mass hypothesis $m_T = 900$ GeV and $m_\phi = 150$ GeV, with a local significance of 2.7 standard deviations. After accounting for the look-elsewhere effect across the 55 tested mass hypotheses, the global significance was reduced to 1.5 standard deviations.
Limits: Upper limits at 95% confidence level were set on the product of the $T\bar{T}$ production cross-section and the branching fraction $\mathcal{B}(T \to \phi t)^2 \mathcal{B}(\phi \to \gamma\gamma)$ . These limits are presented as a function of $m_T$ and $m_\phi$ . While existing LHC searches constrain vector-like top quarks with masses up to about 1.5 TeV for the conventional $T \to Zt, Ht, Wb$ decay modes, this analysis establishes the first exclusion limits for the $T \to \phi t$ topology in the boosted regime.

Significance
The paper claims this analysis constitutes the first exclusive search for pair-produced vector-like top quarks in the boosted regime for the $T \to \phi t$ decay topology. By targeting the diphoton final state, the analysis retains a substantial number of signal events while maintaining good background rejection, despite the potentially small branching fraction of the scalar to diphotons. The results provide new constraints on composite Higgs models and other BSM scenarios predicting vector-like top partners and new scalar bosons, complementing existing limits from conventional decay channels. The methodology, particularly the data-driven background estimation in the presence of boosted topologies, offers a framework for future searches in similar high-mass, multi-body final states.

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