Model-independent measurement of the Higgs boson associated production with two jets and decaying to a pair of W bosons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb⁻¹ of 13 TeV proton-proton collision data collected by the CMS detector, this paper presents a model-independent measurement of the differential production cross section for Higgs bosons decaying to W boson pairs in association with two jets, utilizing a machine learning-derived variable to constrain Higgs couplings within the Standard Model effective field theory framework.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. At CERN, scientists smash these particles together to recreate the conditions of the universe just after the Big Bang. One of the most important "cars" on this track is the Higgs boson, a particle that gives mass to everything else.

This paper is like a detailed detective report from the CMS experiment (one of the giant detectors watching the race). The scientists are trying to understand how the Higgs boson is created when it's accompanied by two "jets" (sprays of particles) and then decays into two other particles (a W boson pair, which quickly turn into an electron, a muon, and some invisible energy).

Here is the story of their investigation, broken down into simple concepts:

1. The Mystery: Is the Higgs Acting "Normal"?

For years, we've known the Higgs boson exists, but we want to know if it behaves exactly as the Standard Model (our current rulebook of physics) predicts, or if it's hiding some "secret rules" from a new, unknown physics.

The scientists focused on a specific clue: the angle between the two jets of particles that appear alongside the Higgs.

• The Analogy: Imagine two people throwing a ball (the Higgs) while standing back-to-back. If they throw it perfectly straight, the angle between them is 180 degrees. If they throw it in a weird, twisted way, the angle changes.
• The Clue: In the Standard Model, the Higgs doesn't care about the angle; the distribution is flat. But if there are "new physics" forces (called Anomalous Couplings) messing with the Higgs, it might prefer certain angles, creating a pattern that looks like a wave or a twist.

2. The Challenge: The "Chameleon" Problem

The biggest problem in this experiment is that the Higgs boson is a chameleon. Its behavior changes depending on what kind of "new physics" might be there.

• The Old Way: Usually, scientists train their computer programs to look for the Higgs based on what the Standard Model says it should look like. But if the Higgs is actually behaving strangely (due to new physics), the computer might miss it or get confused because it was trained on the "normal" version.
• The New Trick (The "Model-Independent" Approach): To solve this, the scientists used a special Artificial Intelligence (AI) technique called Adversarial Deep Learning.
  • The Analogy: Imagine a game of "20 Questions."
    • Player A (The Classifier): Tries to guess if an event is a Higgs or just background noise.
    • Player B (The Adversary): Tries to guess which specific theory the Higgs is following (Standard Model? Weird Physics? Something else?).
  • They train these two AIs against each other. Player A gets punished if Player B can guess the theory. This forces Player A to learn the features of the Higgs that are universal, regardless of whether it's "normal" or "weird."
  • The Result: They created a "universal detector" that can spot the Higgs without needing to know exactly what new physics might be hiding inside it. This makes their measurement much more robust.

3. The Investigation: 138 "Years" of Data

The team looked at data collected between 2016 and 2018.

• The Scale: They analyzed 138 femtobarns of data. To put that in perspective, if you stacked all the collisions they looked at, it would be like watching every single car on Earth drive past a specific point for a very long time.
• The Filter: They had to filter out billions of "junk" collisions (like cars crashing in a parking lot) to find the few hundred that were the specific Higgs events they wanted. They used strict rules: "We need an electron, a muon, missing energy, and two jets."

4. The Findings: "So Far, So Good"

After running their AI and crunching the numbers, they measured how often the Higgs appeared at different angles.

• The Verdict: The results matched the Standard Model predictions almost perfectly. The Higgs boson is behaving exactly as the rulebook says it should.
• The Twist: They did see a tiny hint of something interesting (an asymmetry in the angles), but it wasn't strong enough to be a discovery. It's like hearing a faint whisper in a noisy room; it might be a secret message, or it might just be the wind. Currently, it's just wind.

5. The Future: Tightening the Net

Even though they didn't find "new physics" yet, this paper is a huge success because:

1. It proved the AI trick works: They showed that you can measure particles without biasing the search toward what you expect to find.
2. It set new limits: They drew a very tight circle around the Higgs boson. If there is new physics hiding, it has to be very subtle, because the scientists have now ruled out many of the "loud" possibilities.
3. It constrains the "Wilson Coefficients": In the language of theoretical physics, they put strict limits on the numbers (coefficients) that describe how the Higgs interacts with other particles. Think of it as tightening the screws on the universe's engine to see if anything rattles.

Summary

The CMS team used a clever, unbiased AI to watch the Higgs boson dance with two jets of particles. They checked if the dance steps were weird (indicating new physics). The dance looked perfectly normal. While they didn't find the "new physics" they were hoping for, they proved that their new, unbiased way of looking is incredibly powerful, and they've made the search for the next big discovery even more precise.

In short: The Higgs is behaving itself, but thanks to this paper, we now have a much sharper pair of glasses to catch it if it ever tries to misbehave.

Technical Summary

1. Problem Statement and Motivation

The primary goal of this analysis is to perform a model-independent measurement of the differential production cross-section of the Higgs boson ($H$) decaying into a pair of $W$ bosons ($H \to WW$), specifically in events associated with two jets.

• Physics Context: While the Standard Model (SM) predicts specific properties for the Higgs boson, Beyond-the-Standard-Model (BSM) scenarios suggest the existence of Anomalous Couplings (ACs) in the interaction between the Higgs and vector bosons ($HVV$). These couplings can introduce new tensor structures and potentially violate CP symmetry.
• Key Observable: The signed azimuthal angle difference between the two leading jets, $\Delta\Phi_{jj}$, is a highly sensitive observable for detecting CP-violating effects. In the SM, the distribution is nearly flat. However, pure CP-odd or CP-even anomalous couplings would suppress the cross-section at specific angles ($0, \pm\pi$ or $\pm\pi/2$), and mixed scenarios would create asymmetry.
• The Challenge: Traditional measurements often rely on specific signal hypotheses (e.g., assuming SM kinematics) to extract results. If the true physics differs from the assumption (e.g., BSM effects), the measurement becomes biased. The paper aims to mitigate this by developing a methodology that is agnostic to the signal hypothesis.

2. Methodology

Data and Event Selection

• Dataset: Proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV from 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Final State: The analysis targets the different-flavor dilepton channel ($H \to WW \to e\nu\mu\nu$). Events are selected requiring:
  • One electron and one muon with opposite charges.
  • Two jets with high transverse momentum ($p_T > 30$ GeV) and invariant mass $m_{jj} > 120$ GeV.
  • Missing transverse momentum ($p_T^{miss} > 20$ GeV).
  • Kinematic cuts on transverse mass ($m_T$) and lepton $p_T$ to suppress backgrounds.
• Regions: Events are categorized into a Signal Region (SR) and two Control Regions (CRs) for top quark ($t\bar{t}$) and Drell-Yan ($DY$) backgrounds to constrain normalization.

Model-Agnostic Classification (The Core Innovation)

To maximize model independence, the authors employ an Adversarial Deep Neural Network (ADNN) based on the concept of domain adaptation.

• Architecture: The ADNN consists of two competing networks:
  1. Classifier (C): Trained to distinguish signal (Higgs) from background.
  2. Adversary (A): Trained to predict the specific physics hypothesis (e.g., specific AC values) of the signal events based on the classifier's internal representation.
• Training Strategy: The networks are trained in a competitive loop. The classifier is penalized if the adversary can successfully identify the signal hypothesis. This forces the classifier to learn features that are independent of the specific coupling assumptions, ensuring the output score distribution remains stable across different BSM scenarios.
• Implementation: Two distinct ADNNs were trained:
  • VBF-ADNN: Optimized for Vector Boson Fusion (VBF) production.
  • GGH-ADNN: Optimized for Gluon-Gluon Fusion (ggH) production.
• Input Features: The networks utilize kinematic observables (jet/lepton $p_T$, $\eta$, $\phi$, invariant masses) and Matrix Element (ME) likelihood discriminants to separate signal from background.

Signal Extraction and Unfolding

• Fit Variables: The signal strength is extracted by fitting the ADNN score distributions ($D_{VBF}$ and $D_{ggH}$) in bins of $\Delta\Phi_{jj}$.
• Configurations: Three fit configurations were used:
  1. Combined VBF + ggH cross-section.
  2. Simultaneous measurement of VBF and ggH cross-sections.
  3. VBF cross-section measurement with ggH fixed to SM predictions (to enhance sensitivity to VBF-specific couplings).
• Unfolding: A migration matrix is used within the likelihood fit to correct for detector effects, unfolding the results to the generator-level fiducial phase space.

3. Key Contributions

1. Adversarial Training for HEP: This is a significant application of adversarial domain adaptation in high-energy physics to reduce model bias in differential cross-section measurements. It allows for the reinterpretation of results under various BSM hypotheses without re-running the full analysis.
2. Differential Measurement: Provides the first model-independent differential cross-section measurement of $H \to WW$ with two jets as a function of $\Delta\Phi_{jj}$, covering both VBF and ggH production mechanisms.
3. SMEFT Constraints: The results are reinterpreted within the Standard Model Effective Field Theory (SMEFT) framework to constrain Wilson coefficients for dimension-6 operators.

4. Results

Differential Cross-Sections

• The differential cross-sections were measured in four bins of $\Delta\Phi_{jj}$ ($-\pi$ to $\pi$).
• Significance: The VBF signal was observed with a significance ranging from 1.2 to 3.9 standard deviations ($\sigma$) across the bins. The ggH signal showed lower significance in some bins due to statistical fluctuations and background dominance.
• Asymmetry: The $\Delta\Phi_{jj}$ asymmetry ($A$) was measured to be $-0.43^{+0.27}_{-0.32}$. This is compatible with the SM prediction ($A=0$) with a p-value of 11%, indicating no significant evidence of CP violation in this dataset.

SMEFT Constraints

The measurements were used to constrain Wilson coefficients ($c_i$) in the Warsaw basis:

• VBF Constraints: The most stringent constraints were obtained for the CP-even coefficients $c_{HW}$ and $c_{Hj3}$.
• ggH Constraints: The tightest constraint was found for the CP-even coefficient $c_{HG}$.
• CP-Odd Coefficients: Constraints on CP-odd coefficients (e.g., $c_{\tilde{H}B}$) showed a slight excess (2$\sigma$) in the "float other" scenario, but this is consistent with statistical fluctuations and the 2D constraints.
• Overall Consistency: All measured Wilson coefficients are consistent with the SM expectation (zero) within the 68% and 95% confidence levels.

Model Dependence Assessment

• The study quantified the model dependence of the measurement. Without the ADNN, model dependence could range from 20% to 70%.
• The adversarial approach reduced model dependence by 30–70%, leaving residual dependence primarily due to acceptance effects, which is smaller than the total statistical uncertainty.

5. Significance

This paper represents a major step forward in precision Higgs physics by decoupling the measurement from specific theoretical assumptions.

• Robustness: By using ADNNs, the CMS Collaboration ensures that their differential cross-section measurements remain valid even if the nature of the Higgs boson deviates from the SM in ways not explicitly modeled during training.
• Future Proofing: The model-agnostic results allow for immediate reinterpretation as new BSM theories emerge, without requiring a re-analysis of the raw data.
• CP Sensitivity: The measurement of the $\Delta\Phi_{jj}$ distribution provides a direct probe of CP properties in the Higgs sector. The current results constrain CP-violating effects, though higher luminosity (Run 3 and HL-LHC) will be required to definitively rule out or discover small deviations.

In summary, this analysis successfully demonstrates a robust, model-independent methodology for measuring Higgs boson properties, setting new limits on anomalous couplings and providing a template for future precision measurements in the search for new physics.