Search for Higgs boson pair production in the $\mathrm{b\bar{b}WW}$ decay channel with two leptons in the final state using proton-proton collision data at $\sqrt{s}$ = 13.6 TeV

Using 62 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13.6 TeV collected by the CMS detector, this paper presents the first search for Higgs boson pair production in the $\mathrm{b\bar{b}WW}$ decay channel with two leptons, finding results consistent with the Standard Model and setting an upper limit of 12.0 times the predicted cross section at 95% confidence level.

The Gist

Imagine the universe is a giant, high-stakes billiard game. For decades, physicists have been trying to understand the rules of this game, specifically how the "Higgs boson" (a fundamental particle that gives mass to everything else) behaves.

We know how a single Higgs boson behaves, but we've never seen two of them collide and interact directly. This is like knowing how a single billiard ball rolls, but never having seen two of them bump into each other. Understanding that collision is the key to unlocking the "shape" of the universe's energy landscape.

Here is a simple breakdown of what the CMS team at CERN did in this new paper:

1. The Goal: Catching a "Double Higgs"

The scientists wanted to find evidence of Higgs boson pair production (two Higgs bosons created at once).

• The Analogy: Imagine trying to find a specific, rare double-diamond in a massive pile of gravel.
• The Challenge: These pairs are incredibly rare. In the "standard model" of physics, they should happen about once every few trillion collisions. It's like trying to find a specific grain of sand on a beach by looking at one grain at a time.

2. The New Tool: A Faster, Stronger Collider

This paper is special because it uses data from 2022 and 2023 when the Large Hadron Collider (LHC) was running at a record-breaking energy of 13.6 TeV.

• The Analogy: Previous searches were like trying to find that double-diamond with a flashlight. This new search uses a high-powered searchlight. The higher energy means the "billiard balls" hit harder, making it slightly more likely to create these rare pairs.

3. The Strategy: The "Digital Detective"

Since they can't watch the particles directly (they decay too fast), they look for the "footprints" they leave behind. In this case, they are looking for a specific pattern:

• One Higgs turns into two bottom quarks (which look like jets of particles).
• The other Higgs turns into two W bosons, which then turn into two leptons (like electrons or muons) and some invisible energy (neutrinos).

How they found the signal:

• The Filter: They used a Neural Network (AI). Think of this as a super-smart bouncer at a club. The club is full of "background noise" (common particles like top quarks). The AI was trained to spot the specific "VIPs" (the Higgs pairs) based on their behavior.
• The Upgrade: This time, they didn't just use one bouncer. They used a two-step system. First, a "multiclassifier" sorts the guests into groups. Then, specialized "binary" bouncers check those groups to see if the VIPs are really there. This made the search 50% more sensitive than before.

4. The Results: "No New Physics... Yet"

After analyzing 62 "inverse femtobarns" of data (a massive amount of collision data), here is what they found:

• The Verdict: They did not find a clear signal of Higgs pairs.
• The Good News: The number of events they saw matched the "Standard Model" predictions perfectly. It's like checking your bank account and finding exactly the amount you expected, with no mysterious deposits or withdrawals.
• The Limit: They set a "speed limit" on how often these pairs can happen. They can say with 95% confidence that the rate of Higgs pairs is no more than 12 times what the Standard Model predicts. (Previously, the limit was 14 times).

5. Why This Matters

Even though they didn't find "new physics" (like a new particle), this is a huge success for two reasons:

1. Ruling Out the Wild: By tightening the limit, they are telling theorists, "If you have a theory that predicts Higgs pairs happen 20 times more often than the Standard Model, you are wrong."
2. Testing the "Self-Coupling": The main goal is to measure how Higgs bosons interact with themselves. This interaction determines the stability of the universe. By not finding a huge excess, they are confirming that the universe is stable in the way we currently understand it.

Summary

Think of this paper as a high-tech treasure hunt. The CMS team upgraded their map (better AI), used a stronger metal detector (higher energy), and scoured the beach (more data). They didn't find the treasure (new physics), but they proved that the beach is exactly as empty as the map predicted. This confirms our current understanding of the universe is solid, even if it's not the exciting "new discovery" everyone hopes for.

The Bottom Line: The universe is behaving exactly as the Standard Model says it should, at least when it comes to Higgs boson pairs. The hunt continues, but the rules of the game remain unchanged.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) Higgs mechanism predicts a specific shape for the Higgs potential, which is directly related to the trilinear self-coupling ($\kappa_\lambda$) and the quartic coupling between two Higgs bosons and two vector bosons ($\kappa_{2V}$). While the Higgs boson was discovered in 2012, these self-interactions remain largely unmeasured.

• Objective: To search for non-resonant Higgs boson pair ($HH$) production, specifically targeting the decay channel where one Higgs decays to a bottom quark pair ($b\bar{b}$) and the other decays to two $W$ bosons, which subsequently decay leptonically ($WW \to \ell\nu\ell\nu$).
• Significance: This is the first search for this specific channel using LHC Run 3 data at a center-of-mass energy of 13.6 TeV. It aims to constrain the coupling modifiers $\kappa_\lambda$ and $\kappa_{2V}$, testing the SM prediction where $\kappa_\lambda = \kappa_{2V} = 1$.

2. Methodology and Analysis Strategy

Data and Simulation

• Dataset: Proton-proton collision data collected by the CMS detector in 2022 and 2023, corresponding to an integrated luminosity of 62 fb$^{-1}$ at $\sqrt{s} = 13.6$ TeV.
• Signal Modeling: Simulated using POWHEG (for gluon-gluon fusion, ggF) and MADGRAPH5_aMC@NLO (for vector boson fusion, VBF) at Next-to-Leading Order (NLO) and Leading Order (LO) respectively. Samples were generated for various values of $\kappa_\lambda$ and $\kappa_{2V}$.
• Backgrounds: Dominated by top-quark pair ($t\bar{t}$), single top, and Drell-Yan ($Z/\gamma^* + \text{jets}$) processes. Minor backgrounds include single Higgs production and $VV$/$VVV$ processes.

Event Selection

Events were selected requiring:

• Exactly two opposite-sign leptons ($\mu^+\mu^-$, $e^+e^-$, or $e^\pm\mu^\mp$).
• At least one $b$-tagged jet.
• Kinematic Cuts:
  • Lepton $p_T > 25$ GeV (leading) and $> 15$ GeV (subleading).
  • Invariant mass of the lepton pair ($m_{\ell\ell}$) between 20 and 70 GeV (to suppress $Z \to \ell\ell$).
  • Missing transverse momentum ($p_T^{\text{miss}}$) $> 40$ GeV.
• Validation Regions: Defined with $m_{\ell\ell} > 110$ GeV (enriched in $t\bar{t}$) and $70 < m_{\ell\ell} < 110$ GeV (enriched in Drell-Yan) to constrain background modeling.

Categorization and Machine Learning

A novel staged multiclassification-plus-binary Neural Network (NN) strategy was employed to improve sensitivity by ~50% compared to previous Run 2 analyses:

1. Multiclassification NN ($NN_{\text{cat}}$): Separates events into Signal Regions (SR) targeting ggF or VBF production, or Control Regions (CR) for major backgrounds ($t\bar{t}$, single top, DY, H).
2. Sub-categorization: Events are further split based on jet content:
   • Boosted: Contains a large-radius jet identified as a Lorentz-boosted $H \to b\bar{b}$ candidate.
   • Resolved: Contains exactly 1 $b$-tagged jet ("1b") or $\ge 2$ $b$-tagged jets ("$\ge 2$b").
3. Binary NNs: Dedicated binary classifiers ($NN_{\text{ggF}}$ and $NN_{\text{VBF}}$) are trained within the SRs to distinguish signal from background.
4. Input Variables: The NNs utilize kinematic variables such as the invariant mass of the $b\bar{b}$ system, the $HH$ system mass, $p_T$ of leading jets, and $\Delta R$ separations.

Statistical Analysis

• A simultaneous binned profile likelihood fit was performed using the COMBINE tool.
• Nuisance Parameters: Systematic uncertainties (theoretical cross-sections, jet energy scale, $b$-tagging efficiency, luminosity) were modeled.
• Background Normalization: The normalizations of the dominant $t\bar{t}$ and DY backgrounds were treated as free parameters in the fit, constrained by the validation regions.
• Correction: A data-driven correction was applied to the DY background to correct mismodeling in the jet multiplicity and dilepton $p_T$ spectrum.

3. Key Contributions and Improvements

• First 13.6 TeV Result: This is the inaugural search for $HH \to bbWW$ at the new LHC energy frontier.
• Advanced Classification: The implementation of the staged NN approach (multiclassification followed by binary classification) and the inclusion of dedicated "boosted" categories significantly enhanced sensitivity.
• Trigger Improvements: New trigger strategies for $e^+e^-$ and $e^\pm\mu^\mp$ events increased signal yield by up to 17% in the most sensitive bins.
• Algorithm Updates: Utilization of the PARTICLENET algorithm for $b$-tagging and boosted $H \to b\bar{b}$ identification improved signal-to-background ratios.

4. Results

Signal Observation

• Observation: No significant excess of events over the background-only hypothesis was observed. The data is consistent with SM predictions.
• Goodness-of-Fit: The fit model describes the data well with a $p$-value of 0.19.

Limits on Cross-Section

• Observed Limit: An upper limit on the inclusive $HH$ production cross-section was set at 12.0 times the SM prediction at 95% Confidence Level (CL).
• Expected Limit: The median expected limit was 18.5 times the SM prediction.
• Note: The observed limit is tighter than expected due to a downward fluctuation in the most sensitive signal region (ggF bin 16).

Constraints on Couplings

The results were used to constrain the coupling modifiers:

• Trilinear Coupling ($\kappa_\lambda$): Excluded values outside the range $[-9.1, 15.7]$ (Expected: $[-13.3, 19.8]$) at 95% CL. The best-fit value is $\kappa_\lambda = 3.4$.
• Quartic Coupling ($\kappa_{2V}$): Excluded values outside the range $[-0.20, 2.25]$ (Expected: $[-0.48, 2.54]$) at 95% CL. The best-fit value is $\kappa_{2V} = 1.02$.
• Sensitivity: The analysis shows strong sensitivity to $\kappa_{2V}$, particularly in the boosted regime where selection efficiency increases for non-SM values.

5. Significance

This analysis represents a major step forward in probing the Higgs potential at the LHC. Despite analyzing a smaller dataset (62 fb$^{-1}$) than previous Run 2 searches (138 fb$^{-1}$), the refined analysis strategy and higher collision energy (13.6 TeV) allowed CMS to achieve comparable overall expected sensitivity.

• It provides the first constraints on the quartic Higgs-vector boson coupling ($\kappa_{2V}$) in the $bbWW$ channel.
• It demonstrates the effectiveness of machine learning techniques (staged NNs) in separating complex signal topologies from overwhelming backgrounds.
• The results serve as a critical input for global fits of Higgs couplings and guide future searches in Run 3 and the High-Luminosity LHC era.