Search for resonances decaying to an anomalous jet and a Higgs boson 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 study presents a search for new resonances decaying into a Higgs boson and an anomalous jet identified via an autoencoder, finding no significant excess over Standard Model background and setting the most stringent upper limits to date on the production cross sections for various benchmark scenarios.

The Gist

The Big Picture: Looking for the "Ghost" in the Machine

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful smash-up toy factory. Scientists fire two streams of protons (tiny particles) at each other at nearly the speed of light. Usually, when they crash, they break apart into a predictable shower of known particles (like electrons, quarks, and photons). This is the "Standard Model," which is our current rulebook for how the universe works.

But the rulebook has holes. We don't know what Dark Matter is, or why there is more matter than antimatter. So, the scientists are looking for new, unknown particles that shouldn't exist according to the current rules.

This paper describes a specific search for a "ghost" particle. They aren't looking for just any new particle; they are looking for a specific scenario:

1. A heavy, new particle (let's call it X) is created in the crash.
2. X immediately splits into two things:
   • A Higgs boson (a known particle, like a familiar celebrity).
   • A mysterious second particle (Y), which is the "ghost" they are trying to catch.

The Challenge: The "Speeding Bullet" Problem

Here is the tricky part. The new particle X is very heavy. When it splits, it gives the Higgs and the mystery particle Y a massive kick. They zoom away at incredible speeds (relativistic speeds).

Because they are moving so fast, the debris they leave behind gets squished together.

• Normally, if a particle decays, it might leave two distinct trails.
• But because X is moving so fast, the Higgs and Y look like single, giant, messy blobs (called "large-radius jets") rather than neat, separate tracks.

It's like trying to identify a specific type of fruit that has been smashed into a smoothie. You can't see the individual seeds or skin; you just have a big blob of liquid.

The Strategy: The "Two-Step Detective"

To find this ghost, the CMS team (the scientists) used a clever two-step detective strategy. They treated the two giant blobs differently:

Step 1: The "Higgs" Blob (The Known Celebrity)

One of the blobs is the Higgs boson. The scientists know exactly what a Higgs looks like when it decays (it turns into two bottom quarks).

• The Tool: They used a super-smart AI called ParticleNet.
• The Analogy: Imagine a bouncer at a club who is an expert at recognizing a specific celebrity's face. The AI looks at the "Higgs blob" and says, "Yes, I am 99% sure this is the Higgs celebrity." If the AI isn't sure, they throw that data away. This filters out the noise.

Step 2: The "Mystery" Blob (The Anomaly)

The other blob is the mystery particle Y. The problem is, Y could be anything. It could be a new type of scalar particle, a top quark, or something totally weird. If they built a filter for a specific shape, they might miss the real thing.

• The Tool: They used an Autoencoder (a type of AI that learns to compress and reconstruct images).
• The Analogy: Imagine you train a robot to draw pictures of "normal" clouds. The robot gets really good at drawing fluffy, white, standard clouds.
  • Now, you show the robot a picture of a storm cloud or a cloud shaped like a dragon.
  • The robot tries to draw it based on what it knows (a fluffy cloud). It fails miserably. The difference between what it saw and what it drew is huge.
  • The scientists call this difference the "Anomaly Score." A high score means, "Hey, this blob looks weird! It doesn't look like the normal junk we usually see."

The Search: The "Needle in a Haystack"

The scientists took data from 2016–2018 (138 "inverse femtobarns" of data, which is a fancy way of saying "a massive amount of collision data").

They looked for events where:

1. One blob passed the "Higgs Bouncer" test.
2. The other blob got a high "Anomaly Score" (it looked weird).
3. The total energy of the two blobs matched the mass of a heavy new particle X.

They scanned through millions of collisions, looking for a cluster of these "weird" events in a specific spot on a graph.

The Results: The "Silent Night"

After all that work, the result was: Nothing.

• They didn't find any new particles.
• They didn't see any "ghosts."
• The data looked exactly like what the Standard Model predicted (just normal background noise).

However, this is still a success.
Think of it like searching for a specific type of lost key in a giant field. You didn't find the key, but you proved that the key isn't in the part of the field you searched.

• They set upper limits. This means they can now say, "If this new particle exists, it must be heavier than X or lighter than Y, or it interacts less strongly than Z."
• They ruled out many theoretical models that predicted these particles would be easy to find.

Why This Matters

Even though they found nothing, this paper is a big deal because:

1. It's Model-Independent: They didn't guess what the new particle looked like. They used the "Anomaly Score" to find anything that looked different from the norm. This is like using a metal detector instead of a map; you don't need to know where the treasure is to find it.
2. It's the Best So Far: They set the strictest limits to date on these types of particles.
3. The Tech is Cool: They successfully combined two different AI techniques (one for identifying known things, one for spotting unknown things) to solve a very hard physics problem.

In summary: The scientists smashed protons together, used AI to spot the familiar Higgs boson and a second "weird" blob, and found that the weird blob was just normal background noise. They didn't find new physics this time, but they successfully narrowed the search area for the next time they look.

Technical Summary

1. Problem Statement and Motivation

The Standard Model (SM) of particle physics, while highly successful, cannot explain phenomena such as dark matter or the baryon asymmetry of the universe. This motivates the search for Beyond the Standard Model (BSM) physics.

• Specific Process: The paper targets the resonant production of a heavy BSM particle $X$ that decays into a Higgs boson ($H$) and a second particle $Y$ ($X \to HY$).
• Decay Channels: The Higgs boson is assumed to decay into a bottom quark-antiquark pair ($H \to b\bar{b}$), which is its dominant hadronic decay mode. The particle $Y$ is assumed to decay hadronically into a single large-radius jet.
• Kinematic Regime: The analysis focuses on high-mass scenarios ($M_X > 1.4$ TeV) where both $H$ and $Y$ are highly Lorentz-boosted. This causes their decay products to be collimated, reconstructing as single "fat" jets (large-radius jets, $R=0.8$).
• Challenge: Traditional searches often rely on specific signal models for $Y$. This paper aims to perform a model-independent search for $Y$ by identifying "anomalous" jets that deviate from typical QCD multijet backgrounds, allowing for the simultaneous search of multiple $Y$ decay scenarios (e.g., $Y \to WW$, $Y \to tt$, $Y \to qq$).

2. Methodology

Data and Simulation

• Dataset: 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$^{-1}$.
• Signal Simulation: Simulated using MADGRAPH5_aMC@NLO at Leading Order (LO).
  • Main Benchmark: $X \to H(bb)Y(WW)$, where $Y$ is a scalar decaying to $W^+W^-$. Masses scanned: $M_X \in [1.4, 3.0]$ TeV, $M_Y \in [90, 400]$ GeV.
  • Alternative Benchmarks: $Y \to qq$ (light quarks), $Y \to tt$ (top quark pair), and $Y \to bqq'$ (vector-like quark decay to top).
• Background Simulation: Includes $t\bar{t}$, $W/Z$+jets, QCD multijets, and Higgs production. QCD multijets are the dominant background and are estimated using data-driven methods.

Event Reconstruction and Selection

• Trigger: Requires high-$p_T$ jet activity (single AK8 jet $p_T > 450/500$ GeV or high scalar sum $H_T$).
• Offline Selection:
  • Two leading AK8 jets with $p_T > 300$ GeV and $|\eta| < 2.4$.
  • Dijet invariant mass $M_{jj} > 1300$ GeV.
  • Pseudorapidity separation $|\Delta\eta_{jj}| < 1.3$ to suppress QCD.
  • The Higgs candidate jet must have a "soft-drop mass" between 100–150 GeV.

Machine Learning Techniques

The analysis employs two distinct deep learning algorithms to categorize events:

1. ParticleNet (Targeted Tagging):
   • Purpose: Identify the Higgs candidate jet ($H \to b\bar{b}$).
   • Method: A graph neural network trained to distinguish $b\bar{b}$ jets from QCD jets.
   • Implementation: A mass-decorrelated version is used to ensure background modeling is not biased by the mass spectrum. Events are split into Pass (high score) and Fail (low score) regions.
2. Autoencoder (Anomaly Detection):
   • Purpose: Identify the $Y$ candidate jet as "anomalous" without assuming a specific decay model.
   • Method: A neural network trained on simulated QCD jets to compress and reconstruct them.
   • Anomaly Score: Defined as the mean squared error between the input jet image (32x32 pixel $\eta-\phi$ map) and the reconstructed output. High scores indicate jets with substructures different from QCD (e.g., signal or $t\bar{t}$).
   • Regions: Events are split into Measurement Region (MR) (high anomaly score) and Control Region (CR) (low anomaly score).

Statistical Analysis

• Orthogonal Regions: The analysis defines four regions based on ParticleNet (Pass/Fail) and Autoencoder (MR/CR) scores. The search is performed in the MR Pass region.
• Background Estimation:
  • Non-resonant backgrounds (QCD, $W/Z$+jets) are estimated using a Pass-to-Fail Ratio method. The ratio of distributions between Pass and Fail regions ($R_{P/F}$) is modeled as a polynomial in $M_{jj}$ and $M_Y^j$ and fitted to data in the CR.
  • $t\bar{t}$ and SM Higgs backgrounds are modeled using simulation, normalized to data in specific control regions.
• Fit: A 2D binned maximum likelihood fit is performed in the $(M_{jj}, M_Y^j)$ plane. Systematic uncertainties (luminosity, jet energy scale, tagging efficiencies, PDFs) are included as nuisance parameters.

3. Key Contributions

• Hybrid Search Strategy: Successfully combines a targeted search for the Higgs boson (using ParticleNet) with a model-independent anomaly search for the second particle (using an Autoencoder). This allows sensitivity to a wide range of BSM models in a single analysis.
• First Search for Boosted $Y \to tt$: The paper presents the first search for a Lorentz-boosted top-quark pair ($Y \to tt$) in the context of $X \to HY$ resonances.
• Advanced Background Modeling: Utilizes a robust data-driven Pass-to-Fail ratio method with polynomial modeling to constrain the dominant QCD background, validated in Control Regions.
• Comprehensive Benchmarking: Evaluates performance across four distinct signal topologies ($WW$, $qq$, $tt$, and vector-like quark decays), demonstrating the versatility of the anomaly detection approach.

4. Results

• Observation: No significant excess of events was observed above the Standard Model background expectation in any of the signal regions.
• Local Significance: The largest local fluctuation was found at $M_X = 1600$ GeV and $M_Y = 90$ GeV, with a significance of 2.1 standard deviations, which is consistent with a background fluctuation.
• Exclusion Limits:
  • Main Benchmark ($X \to H(bb)Y(WW)$): 95% Confidence Level (CL) upper limits on the production cross-section $\sigma(pp \to X \to HY) \times \mathcal{B}(H \to bb) \times \mathcal{B}(Y \to WW)$ were set.
    • Limits range from 0.3 fb to 19.1 fb depending on the masses.
    • The most stringent limits (0.3–0.4 fb) are achieved for $M_X \approx 2.2$ TeV and $M_Y \approx 200-250$ GeV.
  • Alternative Benchmarks: Stringent limits were also set for $Y \to qq$, $Y \to tt$, and the vector-like quark scenario ($Y \to bqq'$), representing the most stringent limits to date for these specific processes in the Lorentz-boosted regime.
• Comparison: The analysis sets more stringent limits than previous unsupervised ATLAS searches for similar topologies, primarily due to the high efficiency of the ParticleNet $H \to bb$ tagging, which significantly reduces the background.

5. Significance

This paper represents a significant step forward in model-independent BSM searches at the LHC. By integrating specific Higgs tagging with general anomaly detection, the CMS Collaboration demonstrates a powerful strategy to probe "dark" sectors or complex decay chains without being constrained by specific theoretical assumptions about the new particle $Y$.

• Methodological Impact: The successful application of Autoencoders for jet anomaly detection in a high-mass resonance search validates the use of unsupervised learning in high-energy physics.
• Physics Impact: The exclusion limits constrain a broad class of theoretical models, including the Next-to-Minimal Supersymmetric Standard Model (NMSSM) and models with Vector-Like Quarks, pushing the boundaries of the allowed parameter space for new heavy resonances.
• Future Outlook: The techniques developed here (specifically the combination of targeted and anomaly-based tagging) are directly applicable to future high-luminosity LHC runs and potential future colliders, offering a robust framework for discovering unexpected new physics.