Search for pair production of heavy resonances in final states with a photon and large-radius jets 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 detector, this paper presents the first search for pair-produced heavy resonances decaying into a top quark, a photon, and a gluon, setting 95% confidence level upper limits that exclude spin-1/2 and spin-3/2 t$^*$ particles with masses below 930 GeV and 1330 GeV, respectively, without observing any significant deviation from the background-only hypothesis.

The Gist

The Cosmic Needle in a Haystack: Hunting for "Super-Top" Quarks

Imagine the universe is a giant, high-speed racetrack (the Large Hadron Collider, or LHC) where tiny particles zoom around at nearly the speed of light and crash into each other. Most of the time, these crashes produce particles we already know and understand, like the "Top Quark," which is the heaviest known particle in our standard rulebook (the Standard Model).

But what if there are "Super-Top" quarks? Think of them as the Top Quark's heavier, more energetic cousins that only appear if the universe has hidden rules we haven't discovered yet. This paper is the story of the CMS experiment team at CERN trying to find these elusive "Super-Tops" (called $t^*$).

Here is the breakdown of their quest, explained simply:

1. The Goal: Finding the "Super-Top"

The scientists are looking for a specific scenario: Pair production. Imagine two Super-Tops being born at the same time from a collision.

• The Decay: One Super-Top is expected to break apart into a normal Top Quark and a Gluon (a particle that acts like "glue" holding matter together).
• The Twist: The other Super-Top is expected to break apart into a normal Top Quark and a Photon (a particle of light).

So, the final signature they are hunting for is: Two Top Quarks + One Gluon + One Photon.

2. The Challenge: The "Needle in a Haystack" Problem

Finding this is incredibly hard because:

• The Signal is faint: The "Super-Top" breaking into a Top Quark and a Photon is very rare (like finding a specific grain of sand on a beach).
• The Background is loud: The LHC produces billions of collisions that look almost like what they want, but are just ordinary background noise (like trying to hear a whisper at a rock concert).

3. The Strategy: Using "Super-Brilliant" Light

To cut through the noise, the scientists decided to use the Photon (the light particle) as their guide.

• The Analogy: Imagine you are looking for a specific type of car in a massive, chaotic traffic jam. Most cars are just regular sedans. But you know your target car has a blindingly bright, unique headlight that no other car has.
• By focusing only on collisions that produce this "blinding headlight" (a high-energy photon), they can ignore 99% of the boring, ordinary traffic. This makes the search much cleaner.

4. The Tools: "Smart" Jet Tagging

When a Top Quark is created at these speeds, it doesn't just sit there; it flies off so fast that its decay products (the pieces it breaks into) get squashed together into a single, giant blob of energy called a "Large-Radius Jet."

• The Problem: It's hard to tell if a giant blob of energy is a Top Quark or just a random mess of other particles.
• The Solution: The team used a cutting-edge AI tool called PARTICLENET. Think of this AI as a highly trained detective. Instead of just looking at the size of the blob, it looks at the "texture" and internal structure of the energy, asking, "Does this look like the fingerprint of a Top Quark?"
• This AI is so good that it can spot a Top Quark 82% of the time while rarely getting fooled by fake ones.

5. The Hunt: Reconstructing the Crime Scene

The scientists took data from 2016 to 2018 (a massive amount of information, equivalent to 138 "inverse femtobarns" of collisions). They looked for events where:

1. There was a high-energy photon (the "blinding headlight").
2. There were giant jets of energy.
3. The AI confirmed at least one of those jets was a Top Quark.
4. They combined the energy of the photon and the Top Quark to calculate the mass of the original "Super-Top."

If the Super-Top exists, they should see a "bump" or a spike in the mass graph at a specific weight, rising above the flat line of background noise.

6. The Results: No Super-Tops Found (Yet)

After crunching the numbers, they didn't find the Super-Tops.

• The data looked exactly like what the Standard Model predicted (just background noise).
• There was a tiny, interesting wobble in the data (about 2.5 times what you'd expect by chance), but it wasn't strong enough to claim a discovery. It's like hearing a faint noise in the dark that might be a ghost, but is more likely just the wind.

However, they didn't come up empty-handed.
Because they didn't find the particles, they set limits. They can now say with 95% confidence:

• If a "Spin-1/2" Super-Top exists, it must be heavier than 930 GeV (about 1,000 times the mass of a proton).
• If a "Spin-3/2" Super-Top exists, it must be heavier than 1,330 GeV.

Why This Matters

This is the first time anyone has looked for these specific particles in this specific way (using the photon). Even though the "Super-Top" breaking into a photon is rare, the fact that the background noise is so low makes this search surprisingly powerful.

The Bottom Line:
The universe is still keeping its secrets. The "Super-Top" quarks, if they exist, are hiding in a heavier, more energetic realm than we have reached yet. But thanks to this clever search using "smart" AI and high-energy light, the CMS team has narrowed the hiding spots, telling us exactly where not to look next.

Technical Summary

1. Problem and Physics Motivation

The Standard Model (SM) of particle physics successfully describes most observations but fails to explain fundamental issues such as the hierarchy problem (the vast disparity between electroweak and gravitational forces) and the nature of dark matter. Beyond-the-Standard-Model (BSM) theories, including those involving extra spatial dimensions or composite Higgs scenarios, often predict the existence of excited top quarks ($t^*$) or vector-like top partners ($T$).

• Decay Modes: While vector-like partners typically decay via tree-level processes ($T \to bW, tZ, tH$), these modes can be suppressed if the mixing angle is small. In such cases, loop-induced decays become dominant: $t^* \to tg$ (gluon) and $t^* \to t\gamma$ (photon).
• The Challenge: Previous searches have focused on the $t^*t^* \to ttgg$ channel (assuming $B(t^* \to tg) = 100\%$). However, the $t^* \to t\gamma$ branching fraction is theoretically expected to be small ($\sim 3\%$) compared to $t^* \to tg$ ($\sim 97\%$).
• The Opportunity: Despite the small branching fraction, the $t^*t^* \to tt\gamma g$ channel offers a unique advantage: the presence of a high-energy photon significantly suppresses SM backgrounds compared to the all-hadronic $ttgg$ channel. This paper presents the first search for pair-produced heavy resonances in this specific channel.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS detector from 2016 to 2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Model: Simulated pair production of spin-1/2 and spin-3/2 $t^*$ particles decaying via $t^*t^* \to (t\gamma)(tg)$.
  • Mass points ($m_{t^*}$) range from 700 GeV to 3 TeV.
  • Branching fractions assumed: $B(t^* \to t\gamma) = 3\%$ and $B(t^* \to tg) = 97\%$.
  • Production cross-sections differ by spin (spin-3/2 is $\sim 10\times$ larger than spin-1/2 for the same mass due to spin-dependent couplings).
• Backgrounds: Dominated by $\gamma$+jets (where a jet mimics a top quark) and $t\bar{t}\gamma$. Other contributions include $t\bar{t}$, single top, $W/Z$+jets, and misidentified leptons/hadrons.

Event Reconstruction and Selection

• Trigger: High-$p_T$ photon triggers (thresholds: 175 GeV for 2016, 200 GeV for 2017–2018).
• Object Selection:
  • Photon: Isolated, high-$p_T$ ($>240$ GeV), within the barrel region ($|\eta| < 1.44$).
  • Jets: Large-radius jets (AK8, $R=0.8$) with $p_T > 300$ GeV and $|\eta| < 2.4$.
  • Top Tagging: The PARTICLENET machine-learning tagger (a graph neural network) is used to identify AK8 jets originating from hadronically decaying top quarks.
    • Efficiency: $\sim 82\%$ for true top jets ($400 < p_T < 600$ GeV).
    • Mis-tag Rate: $\sim 0.1\%$ for gluon/light-quark jets.
• Signal Region (SR) Criteria:
  • Exactly one isolated photon ($p_T > 240$ GeV).
  • At least two AK8 jets.
  • One jet ($j_1$) must be top-tagged with a groomed mass ($m_{SD}$) between 125 and 225 GeV.
  • A second jet ($j_2$) must have $m_{SD} > 50$ GeV.
  • No isolated electrons or muons.
• Reconstruction Variable: The invariant mass of the photon and the top-tagged jet ($m_{\gamma j_1}$) is used as the primary discriminant to search for a resonance peak.

Background Estimation

Due to the difficulty in simulating jet misidentification rates accurately, the dominant backgrounds are estimated using data-driven methods:

1. $\gamma$+jets Background: Estimated using a "transfer factor" method. A control region (Application Region) with zero top-tagged jets is used to measure the top-mistag rate ($r$) as a function of jet $p_T$ and $m_{SD}$. This rate is then applied to the Signal Region.
2. Hadron-to-Photon ($h \to \gamma$) Background: Estimated using the "ABCD" method, utilizing sidebands in photon identification variables ($\sigma_{i\eta i\eta}$ and isolation) to measure the misidentification probability.
3. Other Backgrounds: Processes like $t\bar{t}\gamma$ and electron-to-photon ($e \to \gamma$) are estimated using Monte Carlo simulations normalized to data.

3. Key Contributions

• First Search in $tt\gamma g$ Channel: This is the inaugural search for pair-produced excited top quarks in the $tt\gamma g$ final state at the LHC.
• Advanced Tagging: Utilization of the state-of-the-art PARTICLENET algorithm to efficiently identify boosted top quarks within large-radius jets, crucial for reconstructing the heavy resonance mass.
• Robust Background Estimation: Implementation of a rigorous data-driven strategy for the dominant $\gamma$+jets background, overcoming limitations in theoretical modeling of jet substructure and misidentification.
• Spin Sensitivity: The analysis explicitly distinguishes between spin-1/2 and spin-3/2 hypotheses, noting that spin-3/2 production cross-sections are significantly higher.

4. Results

• Observation: No significant excess of events was observed over the Standard Model background expectation.
  • A local deviation of approximately 2.5 standard deviations was noted at high masses, but this is consistent with a statistical fluctuation given the look-elsewhere effect.
• Exclusion Limits (95% Confidence Level):
  • Spin-1/2 $t^*$: Masses below 930 GeV are excluded (Observed: 930 GeV, Expected: 930 GeV).
  • Spin-3/2 $t^*$: Masses below 1330 GeV are excluded (Observed: 1330 GeV, Expected: 1390 GeV).
• Comparison:
  • For spin-1/2, the sensitivity of this $tt\gamma g$ search is competitive with the previous $ttgg$ search (which excluded up to 1050 GeV), despite the much smaller branching fraction ($3\%$ vs $100\%$). This demonstrates the power of the photon signature in reducing backgrounds.
  • For spin-3/2, the limits are slightly lower than the $ttgg$ channel (1330 GeV vs 1700 GeV), but still represent a significant constraint on the parameter space.

5. Significance

This analysis demonstrates that searching for heavy resonances in channels involving high-energy photons is a highly effective strategy, even when the branching fraction is small. The ability to achieve sensitivity comparable to the dominant all-hadronic channel validates the use of photon tagging as a powerful tool for background suppression in BSM searches. The results place stringent constraints on models predicting excited top quarks or vector-like partners, particularly those with suppressed mixing angles that favor loop-induced decays. The methodology established here, particularly the data-driven background estimation and machine-learning-based top tagging, sets a precedent for future searches in complex final states.