Search for Higgs boson production at high transverse momentum in the WW decay channel 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 the first dedicated search for highly Lorentz-boosted Higgs bosons decaying to WW pairs, finding no evidence of a signal above background with a measured signal strength of $\mu$ = $-$0.19$^{+0.48}_{-0.46}$.

The Gist

The Big Picture: Catching a Ghost in a Hurricane

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle accelerator. It smashes protons together at near the speed of light, creating a chaotic storm of debris. In this storm, scientists are looking for a very specific, elusive ghost: the Higgs boson.

We know the Higgs exists (it was found in 2012), but we want to know how it behaves when it's moving incredibly fast. Think of a normal Higgs boson as a slow-moving car. But in this paper, the scientists are looking for a Higgs boson zooming around at 99% the speed of light.

When a Higgs boson moves that fast, it doesn't just decay (break apart) normally. It gets "squished" by the laws of physics (Lorentz contraction). Instead of its decay products flying apart in different directions, they get smashed together into a single, tight bundle.

The Analogy: The "Super-Suitcase"

Normally, if a Higgs boson decays into two W particles (which then decay into other things), it's like opening a suitcase and finding two separate items flying out in opposite directions. Easy to spot.

But when the Higgs is highly boosted (moving super fast), it's like putting those two items into a tiny, high-speed suitcase and throwing it at a wall. When it hits, everything inside is crammed into one tiny, messy pile.

The scientists' job in this paper was to find these "Super-Suitcases" (called large-radius jets) in a massive pile of garbage (background noise) and figure out if any of them contained a Higgs boson.

The Two Detective Teams (The Channels)

The team split the investigation into two groups based on what they found inside the "suitcase":

1. The "One-Lepton" Team (1ℓ): They looked for suitcases that had exactly one "lepton" (a type of particle like an electron or muon) sticking out of the pile.

   • The Challenge: It's hard to tell if that lepton belongs to the Higgs or if it's just a random particle that happened to land there.
   • The Solution: They used a super-smart AI called PART (Particle Transformer). Think of this AI as a master detective who has studied millions of crime scenes. It looks at the tiny details of the particles inside the suitcase and says, "This pattern looks 99% like a Higgs boson!" They even "fine-tuned" this AI specifically to catch the tricky cases where a lepton is hiding inside the jet.

2. The "Zero-Lepton" Team (0ℓ): They looked for suitcases with no leptons sticking out. Everything was hidden inside the pile.

   • The Challenge: This is even harder because the pile looks just like a pile of regular junk (QCD multijets).
   • The Solution: They used a technique called the Lund Jet Plane. Imagine the suitcase is a tree. This technique maps out exactly how the branches (particles) split off from the trunk. They compared the "branching patterns" in their data to what the computer simulations predicted. If the real-world branches matched the Higgs pattern, they counted it.

The "Luggage Tag" Problem

A major issue in this experiment is that the computer simulations (the "theory") aren't perfect. They might predict the suitcase looks a certain way, but in reality, it looks slightly different.

To fix this, the scientists used a reweighting technique. Imagine you have a bag of marbles (simulated data) that you think represents a bag of marbles from a factory (real data). You realize your bag is slightly too heavy. So, you take a scale, weigh a few marbles from the factory, and adjust the weight of your simulated marbles until they match perfectly. This ensures their "Higgs detector" isn't fooled by bad math.

The Result: The Great Silence

After analyzing 138 "inverse femtobarns" of data (which is a fancy way of saying they looked at a massive amount of collision data from 2016–2018), they did the final count.

• What they expected: If the Standard Model (our current best theory of physics) is perfect, they should see a specific number of Higgs bosons.
• What they found: They found zero evidence of extra Higgs bosons. In fact, their best guess was slightly below what was expected (though statistically, this is just a "no signal" result).

The Verdict:
The signal strength was measured as µ = -0.19.

• If µ = 1, it means "We found exactly what the theory predicted."
• If µ = 0, it means "We found nothing."
• If µ = -0.19, it means "We found nothing, and the noise looks slightly like the opposite of a signal."

In plain English: They looked very hard for these high-speed Higgs bosons, used the smartest AI and the best math available, and found nothing new. The data fits perfectly with the Standard Model. There are no "new physics" ghosts hiding in the high-speed suitcases.

Why is this important?

Even though they didn't find a new particle, this is a huge success for science.

1. It's a Stress Test: It proves our current theories (the Standard Model) are incredibly robust. They can predict even the most extreme, high-speed collisions accurately.
2. New Tools: They developed new AI tools (like the fine-tuned PART algorithm) and new calibration methods (Lund Jet Plane) that will be used for future searches.
3. First of its Kind: This was the first time anyone specifically looked for Higgs bosons decaying into W particles when they are moving this fast. It fills a gap in our knowledge, showing us that the Higgs behaves exactly as expected, even when it's running a sprint.

Summary: The scientists ran a high-speed chase for a specific type of Higgs boson. They used AI detectives and advanced math to sift through the debris. They found nothing but the expected background noise, confirming that our current understanding of the universe is still holding up strong, even at the highest speeds.

Technical Summary

1. Problem and Motivation

• Scientific Context: Since the discovery of the Higgs boson ($H$), precision measurements of its properties are crucial. Measuring Higgs production at high transverse momentum ($p_T$) is a critical test of Standard Model (SM) calculations, which involve large logarithmic corrections and higher-order effects in this regime.
• New Physics Potential: Deviations from SM predictions at high $p_T$ could indicate Beyond Standard Model (BSM) physics at energy scales not directly accessible by the LHC.
• The Gap: While high-$p_T$ Higgs searches have been conducted in channels like $H \to b\bar{b}$, $H \to \gamma\gamma$, and $H \to \tau\tau$, this paper presents the first dedicated study of highly Lorentz-boosted Higgs bosons decaying into a pair of $W$ bosons ($H \to WW$).
• Kinematic Challenge: For $p_T^H \gtrsim 250$ GeV, the decay products of the two $W$ bosons are highly collimated, merging into a single large-radius jet ($R=0.8$). This requires specialized reconstruction techniques to distinguish the signal from the overwhelming QCD multijet background.

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: Simulated at Next-to-Leading Order (NLO) accuracy using generators like HJ-MINLO (ggF), POWHEG (VBF, VH, $t\bar{t}H$), and JHUGEN for decay spin correlations.
• Background Simulation: Modeled using MADGRAPH5 aMC@NLO, SHERPA, and POWHEG for QCD multijets, $W/Z$+jets, top quarks, and dibosons.

Event Reconstruction and Categorization

The analysis reconstructs the Higgs candidate as a single large-radius jet (AK8, $R=0.8$) containing the decay products of the $W$ bosons. Events are split into two exclusive channels based on the presence of isolated leptons ($\ell = e, \mu$):

1. 0$\ell$ Channel (Inclusive):

   • Targets fully hadronic ($H \to WW \to qqqq$) and semileptonic decays where the lepton is non-isolated (merged inside the jet).
   • Includes all production modes (ggF, VBF, VH, $t\bar{t}H$).
   • Selection: Requires AK8 jets with $p_T > 400$ GeV and specific mass cuts. Uses missing transverse momentum ($p_T^{miss}$) to identify neutrinos.
   • Background Estimation: Dominated by QCD multijets. Uses a data-driven method with Control Regions (CRs) and polynomial Transfer Functions (TFs) to extrapolate from low-signal regions to Signal Regions (SRs).

2. 1$\ell$ Channel (Exclusive):

   • Targets semileptonic decays ($H \to WW \to \ell\nu qq$) with exactly one isolated lepton.
   • Sub-categorization: Events are further classified into three production modes:
     • Gluon Fusion (ggF): No additional specific topology.
     • Vector Boson Fusion (VBF): Requires two forward jets with large rapidity separation ($|\Delta\eta_{jj}| > 3.5$) and high invariant mass ($m_{jj} > 1$ TeV).
     • Associated Production (VH): Requires a second large-radius jet identified as a hadronically decaying $V$ boson ($W$ or $Z$).
   • Background Estimation: Dominated by $W(\ell\nu)$+jets and $t\bar{t}$. Normalization is constrained using Control Regions enriched in these processes.

Advanced Machine Learning: The PART Algorithm

• Core Technology: The analysis utilizes the Particle Transformer (PART), a deep learning model based on self-attention mechanisms.
• Function: It identifies H-candidate jets by analyzing jet substructure. It outputs 37 classification scores distinguishing between various signal topologies (e.g., $H \to 4q$, $H \to 3q$, $H \to \ell\nu qq$) and backgrounds (QCD, $t\bar{t}$, $W$+jets).
• Fine-Tuning (1$\ell$ Channel): A specific "fine-tuning" strategy was developed for the 1$\ell$ channel. A shallow neural network was trained on the final hidden layer activations of PART to specifically distinguish $H \to \ell\nu qq$ from $W(\ell\nu)$+jets, achieving a 60% increase in signal efficiency at a fixed background efficiency compared to the baseline tagger.
• Calibration: To correct for simulation-data discrepancies, the Lund Jet Plane (LJP) reweighting technique was applied. This method reweights simulated jets based on data-to-simulation ratios of subjet radiation patterns, ensuring the tagger's efficiency is accurately modeled.

Signal Extraction

• Discriminant: The signal is extracted via a binned maximum likelihood fit to the reconstructed invariant mass distribution:
  • 0$\ell$: Corrected jet mass ($m_j^*$), accounting for neutrino momentum.
  • 1$\ell$ (ggF/VBF): Corrected jet mass ($m_j^*$).
  • 1$\ell$ (VH): Soft-drop mass of the associated $V$-candidate jet ($m_V^j$).
• Fit Parameters: The signal strength $\mu$ (ratio of measured cross-section to SM expectation) is the parameter of interest.

3. Key Contributions

1. First Dedicated High-$p_T$ $H \to WW$ Search: This is the inaugural study focusing specifically on the highly boosted $H \to WW$ topology, complementing existing high-$p_T$ results in other channels.
2. Advanced ML Application: Demonstrated the successful application of the Particle Transformer (PART) algorithm for identifying complex jet topologies involving leptons inside jets ($H \to \ell\nu qq$).
3. Transfer Learning Strategy: Introduced a fine-tuning approach for the 1$\ell$ channel to overcome the scarcity of training data for "lepton-in-jet" topologies, significantly improving background rejection.
4. LJP Calibration: Applied the Lund Jet Plane reweighting technique to calibrate the signal efficiency of the machine learning taggers, reducing systematic uncertainties related to jet substructure modeling.
5. Simplified Template Cross Sections (STXS): Results are presented in STXS Stage 1.2 bins, facilitating future combination with other differential measurements.

4. Results

• Signal Strength: The measured signal strength relative to the SM expectation is:
  $$\mu = -0.19^{+0.48}_{-0.46}$$
  This value is consistent with zero and indicates no evidence of a signal above the background.
• Significance:
  • Observed Significance: $0.0\sigma$ (The best-fit value is slightly negative).
  • Expected Significance: $1.86\sigma$.
• Decomposition: The result is consistent with the SM prediction within uncertainties. The observed data lies $2.1$ standard deviations below the SM expectation ($\mu=1$) when allowing for negative signal strengths, but this is not statistically significant.
• Systematics: The dominant uncertainties arise from:
  • 0$\ell$ Channel: Modeling of the QCD multijet background (Transfer Function coefficients).
  • 1$\ell$ Channel: Asymmetric uncertainty in the PART tagger efficiency and limited size of simulated signal samples in the VBF category.

5. Significance

• Validation of SM: The result provides a stringent test of the SM in the high-$p_T$ regime for the $H \to WW$ channel, a region previously unexplored with dedicated techniques.
• Methodological Benchmark: The successful deployment of the Particle Transformer and the LJP reweighting technique sets a new standard for analyzing boosted objects with complex decay topologies (leptons inside jets).
• Future Prospects: While no signal was found, the analysis establishes the necessary tools and frameworks (STXS bins, ML taggers) for future high-luminosity LHC runs (Run 3 and HL-LHC) where increased statistics may reveal deviations from the SM or confirm the SM prediction with higher precision.
• Complementarity: These results fill a critical gap in the global Higgs program, ensuring that the $H \to WW$ channel is not a blind spot in the search for new physics at high energy scales.