Search for a new heavy resonance decaying to a top quark and a neutral scalar boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS detector, this study presents the first fully hadronic search for a heavy vector-like top quark ($\mathrm{T}'$) decaying to a top quark and a neutral scalar boson ($\phi \to b\bar{b}$), setting the most stringent limits to date on $\mathrm{T}'$ masses above 2 TeV and excluding masses between 0.85 and 1.3 TeV for a standard model Higgs boson scenario without observing any significant excess over background predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle smash-up. Scientists fire protons at each other at nearly the speed of light, hoping that the resulting explosion will reveal new, hidden particles that don't exist in our everyday world.

This paper is a report from the CMS Collaboration, one of the two giant teams of scientists working at the LHC. They are hunting for a specific type of "ghost" particle: a heavy, hypothetical partner to the top quark (the heaviest known particle in the Standard Model), which they call T'.

Here is the story of their hunt, explained simply:

1. The Mystery: Why do we need a new particle?

Think of the Standard Model (our current rulebook for physics) as a very good, but slightly broken, scale. It works great for most things, but it has a glitch: it can't explain why the Higgs boson (the particle that gives other particles mass) is so light. It's like trying to balance a feather on a scale that keeps tipping over because of invisible quantum "noise."

To fix this, scientists propose new theories involving Vector-Like Quarks (VLQs). Imagine these as "bodyguards" for the top quark. They are heavy, mysterious partners that might explain the glitch. If they exist, they should be heavy enough to be created only in the most violent collisions at the LHC.

2. The Hunt: What are they looking for?

The scientists are looking for a specific "signature" of a T' particle dying.

• The Scenario: A heavy T' particle is created and immediately splits apart.
• The Split: It breaks into two things:
  1. A Top Quark (which then decays into other particles).
  2. A Neutral Scalar Boson (ϕ). This is a new, invisible particle. The scientists suspect it might turn into a pair of "bottom quarks" (heavy cousins of the top quark).

The Challenge: Because the T' is so heavy, the particles it spits out are moving incredibly fast—like a bullet fired from a gun. When they move that fast, their decay products (the smaller pieces they break into) get squished together. Instead of seeing a messy pile of debris, the detector sees two giant, fat "jets" of particles.

3. The Detective Work: Sorting the Noise

The LHC is a noisy place. Every second, billions of collisions happen, but 99.9% of them are just "background noise" (like regular QCD jets or top quark pairs that happen naturally). Finding the T' is like trying to find a specific, rare coin in a massive pile of identical-looking rocks.

To do this, the CMS team used two main tools:

• The "Jet" Filter: They looked for those two giant, fat jets mentioned above.
• The "AI" Tagger (PARTICLENET): This is the star of the show. They trained a sophisticated Artificial Intelligence (a neural network) to look at the "substructure" inside those fat jets.
  • Analogy: Imagine you have two bags of fruit. One bag has a mix of apples and oranges (the background noise). The other bag has a specific, rare fruit salad (the signal). The AI is like a super-smart fruit inspector that can look inside the bag and say, "This bag definitely has the rare fruit salad," even if the fruits are mashed together.

4. The Strategy: Two Channels

The scientists didn't just look at one type of collision. They looked at two different ways the top quark could decay:

1. The "Fully Hadronic" Channel (This Paper): Everything turns into jets (particles that look like fireballs). This is the "all-or-nothing" approach. It's harder to find because there's so much background noise, but it catches more events.
2. The "Semileptonic" Channel (Previous Work): One part of the decay turns into a charged particle (like an electron or muon) and a neutrino. This is cleaner and easier to spot, but it happens less often.

In this paper, they combined the results of both searches to get the strongest possible answer.

5. The Results: The "Ghost" Remains Elusive

After analyzing a massive amount of data (138 "inverse femtobarns"—which is a fancy way of saying they looked at trillions of collisions from 2016 to 2018), here is what they found:

• No Ghosts Found: They did not see any significant excess of events. The data looked exactly like the "background noise" they expected. There was no sign of the T' particle.
• Setting the Limits: Even though they didn't find it, they learned something important. They can now say with 95% confidence: "If this T' particle exists, it cannot be lighter than 1.3 TeV (for certain scenarios)."
  • Analogy: Imagine you are looking for a specific type of fish in a lake. You don't find it. You can't say the fish doesn't exist, but you can say, "If it's there, it's not in the shallow water; it must be deeper than 100 feet."
• The Best Limits Yet: For heavy particles (above 2 TeV), this search sets the strictest limits in the world so far. They have pushed the "exclusion zone" further than anyone else has before.

6. The Takeaway

This paper is a testament to the power of modern particle physics. Even though they didn't find the new particle they were hunting for, they successfully ruled out a huge range of possibilities.

• Why does this matter? By ruling out where the particle isn't, they are forcing theorists to rewrite their theories. If the T' particle exists, it must be heavier or behave differently than previously thought.
• The Future: The hunt continues. The LHC is getting stronger, and the detectors are getting smarter. The scientists are essentially saying, "We haven't found the needle in the haystack yet, but we've checked the bottom half of the haystack very thoroughly. Now we need to look deeper."

In short: No new heavy particles were found, but the search has become much more precise, narrowing the search area for the next generation of experiments.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics faces the hierarchy problem, specifically regarding the stability of the Higgs boson mass against quantum corrections. Beyond-the-Standard-Model (BSM) theories, such as those introducing Vector-Like Quarks (VLQs), offer potential solutions.

• The Signal: This paper searches for a hypothetical heavy vector-like top quark partner ($T'$) produced singly in association with a bottom quark ($b$). The $T'$ decays into a standard top quark ($t$) and a new neutral scalar boson ($\phi$).
• The Decay Chain: The analysis focuses on the fully hadronic final state where:
  • The top quark decays hadronically ($t \to bW \to bqq'$).
  • The scalar boson $\phi$ decays to a bottom-antibottom pair ($\phi \to b\bar{b}$).
• Kinematic Regime: The search targets high-mass $T'$ resonances ($0.8 - 3$ TeV). In this regime, the decay products are highly Lorentz boosted, causing the decay products of the top quark and the $\phi$ boson to merge into single, large-radius jets. This creates a distinct dijet topology.
• Gap in Previous Searches: While previous searches focused on $T'$ decays to SM bosons ($W, Z, H$), this work specifically targets decays to new scalar/pseudoscalar particles, a scenario motivated by extended Higgs sectors (e.g., Two-Higgs-Doublet Models with VLQs).

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS detector during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Simulation: Generated using MADGRAPH5_aMC@NLO at leading order. The $T'$ is modeled as a weak-isospin singlet with a width of 1% or 5% of its mass. Signal mass points ($m_{T'}$) range from 0.8 to 3 TeV, and scalar masses ($m_\phi$) range from 75 to 500 GeV. Interpolation techniques are used to fill gaps in the mass grid.
• Background Simulation:
  • $t\bar{t}$ (Top pair): Simulated with POWHEG v2 (NLO) + PYTHIA 8. This is the dominant background.
  • QCD Multijet: Simulated with MADGRAPH5_aMC@NLO (LO).
  • V+jets: Simulated with MADGRAPH5.

Event Selection and Reconstruction

• Triggers: Multi-level triggers based on the scalar sum of transverse momenta ($H_T$) of AK8 jets and specific jet mass requirements.
• Jet Clustering: Events require at least two AK8 jets (large-radius jets, $R=0.8$) with $p_T > 350$ GeV and $|\eta| < 2.4$.
• Jet Substructure:
  • Soft-Drop Mass: Applied to remove soft/collinear radiation and define the jet mass.
  • Machine Learning Taggers: The PARTICLENET algorithm (a dynamic graph convolutional neural network) is used to distinguish signal jets from background.
    • $t$-tagger ($TPNet_{bqq}$): Discriminates hadronic top decays from light quarks/gluons.
    • $\phi$-tagger ($TX_{bb}$): A mass-decorrelated discriminant identifying jets from $b\bar{b}$ decays (mimicking $\phi \to b\bar{b}$).

Analysis Regions

Events are categorized into three regions based on tagger scores:

1. Signal Region (SR): One jet passes the high-purity (HP) $t$-tagger ($TPNet_{bqq} \geq \text{HP}$) and the other passes the HP $\phi$-tagger ($TX_{bb} > 0.98$).
2. Control Region for QCD (CR(QCD)): The $t$-tagger requirement is inverted (low-purity) to estimate the QCD multijet background.
3. Control Region for $t\bar{t}$ (CR($t\bar{t}$)): Used to constrain systematic uncertainties on the $t\bar{t}$ background.

Background Estimation Strategy

• QCD Multijet: Estimated using a data-driven method. A transfer function (TF) is derived from the ratio of events passing vs. failing the $\phi$-tagger in the QCD-enriched control region. This TF is applied to the "Fail" region of the Signal Region to predict the "Pass" (signal) QCD background.
• $t\bar{t}$ and V+jets: Estimated using Monte Carlo simulation, normalized and shaped by the fit.
• Statistical Model: A 2D binned likelihood fit is performed in the plane of the reconstructed scalar mass ($m^{rec}_\phi$) and the reconstructed $T'$ mass ($m^{rec}_{T'}$). The fit simultaneously analyzes the Signal Region and the $t\bar{t}$ Control Region to constrain systematic uncertainties.

Combination

The results of this fully hadronic search are combined with a previous CMS search in the semileptonic channel (where the top decays to a lepton). The combination uses a simultaneous maximum likelihood fit, treating common systematic uncertainties (e.g., jet energy scale, luminosity) as correlated and channel-specific uncertainties as uncorrelated.

3. Key Contributions

1. First Search of its Kind: This is the first LHC search for a vector-like top quark decaying into a top quark and a new neutral scalar boson (BSM scalar) in the fully hadronic channel.
2. Advanced Tagging: Utilization of the PARTICLENET deep learning algorithm with mass-decorrelated discriminants to efficiently identify boosted $t \to bqq'$ and $\phi \to b\bar{b}$ topologies while minimizing bias in background mass distributions.
3. Robust Background Estimation: Implementation of a data-driven transfer function method for the dominant QCD multijet background, validated in control regions, reducing reliance on simulation for the most challenging background.
4. Comprehensive Combination: The first combination of fully hadronic and semileptonic channels for this specific BSM decay mode ($T' \to t\phi$), significantly improving sensitivity, particularly at lower masses.

4. Results

• Observation: No significant excess of events was observed over the Standard Model background prediction in the 2D $(m^{rec}_{T'}, m^{rec}_\phi)$ plane. The data are consistent with the background-only hypothesis.
• Exclusion Limits (SM Higgs Case):
  • Assuming the scalar $\phi$ is the SM Higgs boson ($m_H = 125$ GeV) and the $T'$ width is 5% of its mass:
    • $T'$ masses between 0.85 and 1.3 TeV are excluded at 95% Confidence Level (CL).
    • This improves upon previous CMS limits by up to a factor of three.
    • For masses above 2 TeV, these represent the most stringent limits to date.
• General Limits:
  • Upper limits on the product of the production cross-section and branching fraction ($\sigma \times \mathcal{B}$) were set for various $m_\phi$ and $m_{T'}$ combinations.
  • Limits as low as 0.1 fb were achieved for certain mass points.
  • The combination of channels improved the upper limits by up to a factor of two for $m_{T'} < 1.5$ TeV compared to the hadronic channel alone.

5. Significance

• BSM Constraints: The results place stringent constraints on models predicting vector-like quarks that couple to extended Higgs sectors (e.g., 2HDM + VLQ). The exclusion of $T'$ masses up to 1.3 TeV (and limits extending to 3 TeV) significantly narrows the parameter space for these theories.
• Methodological Benchmark: The successful application of deep learning taggers (PARTICLENET) and data-driven background estimation in a fully hadronic, high-mass resonance search sets a new standard for future BSM searches at the LHC, particularly for scenarios involving highly boosted objects.
• Future Prospects: The analysis demonstrates the viability of searching for new scalars in the fully hadronic channel, a regime previously dominated by QCD background. The techniques developed here are directly applicable to Run 3 and the High-Luminosity LHC (HL-LHC) era, where higher statistics will allow for even tighter constraints or potential discovery.