Particle transformers for identifying Lorentz-boosted Higgs bosons decaying to a pair of W bosons

This paper introduces the Particle transformer (PaRT), a novel deep neural network based on self-attention that achieves high-efficiency tagging of Lorentz-boosted Higgs bosons decaying to W boson pairs in CMS data while maintaining decorrelation from jet mass, thereby enhancing the sensitivity of Standard Model measurements and beyond-the-Standard-Model searches.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle-smashing machine. When protons collide at nearly the speed of light, they create a chaotic explosion of thousands of tiny particles. Physicists need to sift through this cosmic debris to find rare, precious "treasures"—like the Higgs boson—hidden among a mountain of ordinary "junk" (common particles).

This paper introduces a new, super-smart digital detective called PART (Particle Transformer) that helps the CMS experiment find a very specific, hard-to-spot treasure: a Higgs boson that has decayed into two W bosons, which then turn into a spray of four quarks.

Here is the breakdown of how this works, using simple analogies:

1. The Problem: Finding a Needle in a Haystack

When a Higgs boson is created with high energy, it zooms away so fast (it's "Lorentz-boosted") that its decay products get squished together. Instead of seeing four separate particles flying apart, they merge into a single, messy "jet" of energy.

• The Analogy: Imagine you are trying to identify a specific type of fruit salad (the Higgs) by looking at a single, giant, blended smoothie cup (the jet). The problem is that the background noise (QCD jets) is like millions of cups of plain, muddy water that look almost exactly like your fruit smoothie. Traditional methods are like trying to guess the ingredients by just looking at the color of the cup; they often get it wrong.

2. The Solution: The "Particle Transformer" (PART)

The CMS team built a new Artificial Intelligence (AI) called PART. Unlike older AI models that looked at the jet as a blurry 2D picture (like a photograph), PART looks at the jet as a list of individual ingredients.

• The Analogy:
  • Old AI (DEEPAK8): Like a security guard looking at a blurry photo of a crowd and guessing who the VIP is based on the general shape of the group.
  • PART: Like a master chef who can taste every single grain of salt, every slice of apple, and every drop of juice in the smoothie. It uses a "self-attention" mechanism, which is like the chef asking, "How important is this specific cherry compared to that specific strawberry?" It weighs the importance of every single particle to understand the whole picture.

3. The Training: Learning from a "Cosmic Kitchen"

To teach PART how to spot this specific Higgs decay, the scientists didn't just show it real data. They created a massive "training kitchen" using supercomputers.

• The Recipe: They simulated millions of collisions, creating Higgs bosons that decayed in weird ways (sometimes into 3 particles, sometimes 4, sometimes with different masses).
• The Challenge: The Higgs boson decaying into W bosons is tricky because the W bosons are heavy and behave differently depending on how fast the Higgs is moving.
• The Fix: The scientists taught PART to ignore the specific "weight" of the fruit salad and focus on the pattern of the ingredients. This ensures that when PART sees a real Higgs, it doesn't get confused just because the Higgs is moving slightly faster or slower than the ones it saw in training.

4. The Calibration: Checking the Taste with "Lund Jet Planes"

Even the best AI can be slightly off when moving from computer simulations to real-world data. To fix this, they used a technique called the Lund Jet Plane.

• The Analogy: Imagine PART is a new wine taster. You trust its judgment, but you want to make sure it's not biased by the computer simulation. So, you compare its tasting notes against a "standard reference wine" (a known, abundant particle process) that you know well.
• The Result: They found that PART's "taste" in the real world was 90% to 100% accurate compared to the simulation. They applied a small "correction factor" (like adding a pinch of salt) to ensure the results are perfectly calibrated.

5. The Results: A Super-Sensitive Detector

The new PART algorithm is a game-changer:

• Efficiency: It successfully identifies the Higgs boson decay more than 50% of the time (a huge improvement).
• Precision: It rejects the background "junk" (mistaking mud for fruit) with incredible accuracy, only making a mistake 1 time out of 100.
• Speed: It is actually faster to run than previous models, despite being more complex.

Why Does This Matter?

This isn't just about finding one particle. By getting better at spotting these specific "four-quark" jets, physicists can:

1. Measure the Higgs more precisely: Understanding how the Higgs interacts with itself (a property called "quartic coupling") is crucial for understanding why the universe has mass.
2. Search for New Physics: If there are heavier, unknown particles (like "Heavy Higgs" or other new theories) that decay into similar patterns, PART is now sensitive enough to spot them.

In summary: The CMS collaboration has upgraded its digital eyes. They replaced a blurry camera with a high-definition, ingredient-by-ingredient scanner. This new "Particle Transformer" allows them to find rare cosmic treasures in the chaos of particle collisions with unprecedented speed and accuracy, opening the door to discovering the secrets of the universe.

Technical Summary

1. Problem Statement

The identification of hadronic decays of highly Lorentz-boosted resonances is a critical challenge in high-energy physics, particularly for the CMS experiment at the LHC. While previous deep learning (DL) models (e.g., DeepAK8, ParticleNet) have successfully identified two-pronged jets (e.g., $H \to b\bar{b}$ or $H \to c\bar{c}$), identifying four-pronged jets from the decay chain $H \to WW^* \to 4q$ has remained difficult.

Key challenges include:

• Complex Topology: The decay involves four quarks, often resulting in asymmetric kinematics and varying numbers of resolved subjets (3-pronged vs. 4-pronged) depending on the boost.
• Background Rejection: Distinguishing these signal jets from the overwhelming Quantum Chromodynamics (QCD) multijet background and top quark ($t \to Wb$) backgrounds.
• Calibration Difficulty: Unlike $H \to b\bar{b}$, where $Z \to b\bar{b}$ jets serve as a proxy for calibration, there is no abundant, high-purity Standard Model (SM) proxy for four-pronged $H \to WW^*$ jets.
• Mass Decorrelation: Taggers must be decorrelated from jet mass to allow for data-driven background estimation using sideband regions, a requirement often difficult to meet when training on specific resonance masses.

2. Methodology

A. The Particle Transformer (PART) Architecture

The authors introduce PART, a novel deep neural network based on the Particle Transformer architecture.

• Input: The model processes a set of input tokens comprising Particle Flow (PF) candidates (up to 128 per jet) and Secondary Vertices (SVs) (up to 10 per jet).
• Mechanism: It utilizes Self-Attention mechanisms (specifically Particle Attention Blocks - PABs) to weigh the importance of different particles and their pairwise relationships.
• Features: Inputs include kinematic variables ($p_T$, $\eta$, $\phi$, mass), particle identification (charge, type), track quality, and impact parameters. Pairwise features ($\ln \Delta R$, $\ln k_T$, $\ln z$, $\ln m^2$) are embedded and used as attention biases.
• Output: The model performs a 37-class multiclass classification (covering various $H$, $t$, and QCD decay modes with different flavor compositions) and an auxiliary mass regression task.

B. Training Strategy and Decorrelation

To ensure the tagger is robust and decorrelated from jet mass:

• Broad Mass Sampling: Training samples are generated using a spin-2 resonance ($G \to HH$) and a spin-0 resonance ($Z' \to t\bar{t}$) with masses varied over wide ranges ($m_G, m_{Z'} \in [600, 6000]$ GeV).
• Variable $W$ Mass: Crucially, for $H \to WW^*$ training, the $W$ boson mass ($m_W$) is varied relative to the Higgs mass ($m_H$) to prevent the model from learning specific kinematic phases (off-shell vs. on-shell) that depend on fixed mass ratios.
• Loss Function: The model minimizes a combined loss: Cross-Entropy for classification and Log-Cosh for mass regression.
• Data Volume: Trained on 52.4 million simulated jets using the WEAVR framework on PyTorch.

C. Calibration via Lund Jet Plane (LJP)

Due to the lack of a direct SM proxy for $H \to WW^*$, the authors employ a novel calibration technique based on the Primary Lund Jet Plane (LJP):

• Concept: The LJP maps the radiation pattern of a jet in the $(\ln(1/\Delta), \ln(k_T))$ plane.
• Procedure: Data-to-simulation density ratios of primary LJP splittings are measured in a control sample of boosted $W \to q\bar{q}$ jets (from top quark decays). These ratios are used to derive event weights for $H \to WW^*$ signal jets, correcting for mismodeling in the substructure of the simulated jets.
• Validation: The method is validated on boosted top quark jets, showing improved agreement between data and simulation compared to previous methods.

3. Key Contributions

1. First Identification of $H \to WW^* \to 4q$: This paper presents the first application of a DL tagger specifically optimized for identifying all-hadronic boosted Higgs decays to $WW^*$ in the CMS experiment.
2. Superior Performance: PART significantly outperforms the previous state-of-the-art mass-decorrelated algorithm (DeepAK8-MD).
3. Novel Calibration: The introduction of the LJP-based calibration method for multiprong jets, overcoming the lack of a direct SM proxy.
4. Mass Decorrelation: Achieves strong tagging performance while maintaining decorrelation from jet mass without using adversarial training, relying instead on broad mass sampling in the training set.

4. Results

Performance Metrics

• Efficiency vs. Background: PART achieves a tagging efficiency of >50% for $H \to WW^* \to 4q$ jets at a QCD background efficiency of 1%.
• Improvement over Baseline: Compared to DeepAK8-MD, PART offers:
  • Up to 10x stronger rejection of QCD multijet backgrounds.
  • Up to 8x stronger rejection of top quark backgrounds.
• Mass Resolution: PART demonstrates improved mass resolution (FWHM) for $H \to WW^*$ and $t \to bqq$ jets compared to Soft-Drop and ParticleNet algorithms.

Calibration and Uncertainties

• Scale Factors (SF): Data-to-simulation selection efficiency scale factors were measured in the range 0.9–1.0.
• Uncertainties: Relative uncertainties on these scale factors range from 7% to 23%, dominated by uncertainties in the number of prongs and the extrapolation of LJP corrections to high $p_T$.
• Validation: The LJP calibration reduced the $\chi^2$ discrepancy between data and simulation for boosted top quark jets from 20.7 to 16.6.

Physics Application

The algorithm was applied to the first search for Standard Model Higgs pair ($HH$) production in the all-hadronic $bbWW$ decay mode.

• The enhanced sensitivity of PART allows for tighter constraints on the quartic Higgs-vector boson coupling ($\kappa_{2V}$).
• The dominant systematic uncertainty in this search is the statistical uncertainty of the QCD background, followed by the 15–25% uncertainty in the PART signal efficiency.

5. Significance

This work represents a major advancement in jet substructure analysis at the LHC:

• New Physics Reach: It enables the exploration of BSM scenarios involving heavy Higgs bosons, two-Higgs-doublet models, and resonances decaying to boosted vector boson pairs, which were previously inaccessible due to poor background rejection.
• SM Precision: It provides a powerful tool to constrain the quartic Higgs coupling, a fundamental parameter of the Standard Model that is difficult to measure.
• Methodological Shift: The successful application of the Particle Transformer architecture and the LJP-based calibration sets a new standard for identifying complex, multi-pronged hadronic final states, moving beyond simple image-based or graph-based approaches to true set-based attention mechanisms.

In summary, the CMS Collaboration has successfully deployed a state-of-the-art Particle Transformer to identify a previously elusive Higgs decay mode, significantly enhancing the sensitivity of searches for both Standard Model and Beyond-the-Standard-Model physics.