Measurements of the Higgs boson production, fiducial and differential cross-sections in the four lepton decay channel using 164 fb$^{-1}$ of data collected at $\sqrt{s}$ = 13.6 TeV with the ATLAS detector

Using 164 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13.6$ TeV collected by the ATLAS detector, this paper presents inclusive, differential, and production-mode cross-section measurements of the Higgs boson in the $H \to ZZ^{*} \to 4\ell$ decay channel, yielding results consistent with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It takes tiny protons and smashes them together at nearly the speed of light, creating a chaotic explosion of new particles. Among the trillions of collisions, scientists are hunting for a very specific, rare "ghost": the Higgs boson.

This paper is a report from the ATLAS experiment, one of the giant detectors at the LHC. The team has collected a massive amount of data (164 "inverse femtobarns"—a unit of data volume that is roughly equivalent to watching a high-definition movie 100,000 times over) from collisions at a record-breaking energy level of 13.6 TeV.

Here is what they found, explained through simple analogies:

1. The Hunt: Finding a Needle in a Haystack

The Higgs boson is unstable; it falls apart almost instantly. The scientists are looking for a specific way it breaks down: into four "leptons" (which are like electrons and muons). Think of the Higgs boson as a fragile glass vase that shatters into four specific colored marbles.

• The Challenge: The "haystack" is filled with other particles that look like these four marbles but aren't from the Higgs. These are "background noise."
• The Solution: The ATLAS detector is like a super-precise camera that can track the speed and path of every single marble. By using advanced math and artificial intelligence (specifically a "neural network" that acts like a highly trained detective), the team can filter out the fake marbles and isolate the real Higgs events.

2. The Main Discovery: The "Goldilocks" Result

The team measured how often this Higgs boson is created (the "cross-section").

• The Prediction: The Standard Model (our current best theory of physics) predicted a specific number of Higgs events, like a weather forecast predicting 100 inches of rain.
• The Measurement: The ATLAS team counted the actual events. They found 3.65 (with a small margin of error).
• The Verdict: The Standard Model predicted 3.68.
• The Analogy: Imagine a baker predicts a cake will weigh 3.68 kg. When they weigh the actual cake, it is 3.65 kg. The difference is so tiny it's likely just a scale fluctuation. The result is a perfect match. The Higgs boson behaves exactly as the Standard Model says it should.

3. Looking at the Details: The "Portrait" vs. The "Snapshot"

The scientists didn't just count the total number of Higgs bosons; they looked at how they were made and how they moved.

• Differential Measurements: They looked at the Higgs boson's speed, direction, and the energy of the particles it produced. It's like taking a high-definition portrait of the Higgs rather than just a blurry snapshot. They checked if the Higgs was moving too fast or if it was spinning strangely.
• The Result: Every detail of the "portrait" matched the Standard Model's drawing. There were no weird distortions or unexpected features.

4. How Was It Made? The "Production Modes"

The Higgs boson can be created in a few different ways, like a car being built in different factories:

• Glue Factory (ggF): Two gluons smash together.
• Vector Factory (VBF): Two other particles fuse.
• Heavy Truck Factory (ttH): A top quark and anti-quark pair create it.

The team separated the data into these different "factories" to see if one was producing more or fewer Higgs bosons than expected.

• The Result: All factories are producing the Higgs boson at the exact rate predicted by the theory.

5. The "What If" Scenarios: Testing the Rules

Since the results match the Standard Model so perfectly, the scientists asked: "What if the rules are slightly different?" They tested two main ideas:

• The "Knob" Theory (Couplings): Imagine the Higgs has knobs that control how strongly it interacts with other particles. The team turned these knobs in their computer models to see if the data would fit better with a different setting.
  • Result: The knobs are set exactly to the "Standard Model" position. No new settings were needed.
• The "Hidden Force" Theory (EFT): They looked for subtle signs of new physics that might be hiding in the data, like a faint whisper in a noisy room.
  • Result: No whispers were heard. The data is consistent with our current understanding of the universe.

6. The "Self-Love" of the Higgs

Finally, they looked at the Higgs boson's "self-coupling"—how it interacts with itself. This is a very difficult measurement, like trying to hear two people whispering to each other in a crowded stadium.

• The Result: The data is consistent with the Standard Model's prediction for this interaction, though the measurement is still a bit "fuzzy" (has a large margin of error) because the effect is so rare.

The Bottom Line

This paper is a massive victory for the Standard Model. After smashing protons at record energies and analyzing 164 units of data, the ATLAS team found that the Higgs boson is behaving exactly as we predicted it would.

Think of it this way: If the Standard Model is a map of a city, this paper is a GPS check that confirms every street, building, and traffic light is exactly where the map says it is. While this might sound boring to some (because we didn't find a "new city" or "alien technology"), in physics, confirming the map is accurate is a huge achievement. It tells us that our current understanding of the universe is solid, even if it means we have to look even harder to find the next big discovery.

Technical Summary

Technical Summary: Measurements of Higgs Boson Production and Cross-Sections in the $H \to ZZ^* \to 4\ell$ Channel

Problem and Motivation
This paper presents a comprehensive measurement of Higgs boson production properties using proton–proton collision data collected by the ATLAS detector at the Large Hadron Collider (LHC). The analysis utilizes an integrated luminosity of 164 fb$^{-1}$ recorded between 2022 and 2024 at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV. The study focuses on the $H \to ZZ^* \to 4\ell$ decay channel ($\ell = e, \mu$), which offers a clean experimental signature with excellent signal-to-background ratios and full kinematic reconstruction. While previous measurements at $\sqrt{s}=13$ TeV (Run 2) established the Higgs boson's properties, this work aims to provide the most precise ATLAS measurements at 13.6 TeV to date, testing the Standard Model (SM) with improved statistical power and refined analysis techniques.

Methodology
The analysis employs two complementary frameworks to measure cross-sections:

1. Fiducial and Differential Cross-Sections:

   • Selection: Events are selected based on four reconstructed charged leptons (electrons and muons) forming two same-flavour, opposite-charge pairs. Kinematic requirements include lepton transverse momentum thresholds, invariant mass windows around the $Z$ boson mass, and vertex compatibility.
   • Background Estimation: The dominant background, continuum $ZZ^*$ production, is constrained directly from data using sideband regions ($105 < m_{4\ell} < 115$ GeV and $130 < m_{4\ell} < 160$ GeV). Backgrounds with non-prompt leptons (from $Z$+jets, $t\bar{t}$, $WZ$) are estimated using a data-driven fake-factor method.
   • Unfolding: Inclusive and differential cross-sections for eight observables ($p_T^{4\ell}$, $|y^{4\ell}|$, $m_{12}$, $m_{34}$, $N_{jets}$, $|\Delta\phi_{jj}|$, $\phi$, and a double-differential $p_T^{4\ell}$ vs. $m_{34}$) are extracted via binned maximum-likelihood fits to the reconstructed $m_{4\ell}$ spectrum. Detector effects are corrected using a matrix unfolding procedure to obtain particle-level results within a well-defined fiducial phase space.

2. Production-Mode Cross-Sections (STXS):

   • Categorization: Events are assigned to mutually exclusive categories based on jet multiplicity ($N_{jets}$), Higgs transverse momentum ($p_T^H$), and dijet invariant mass ($m_{jj}$).
   • Multivariate Analysis: To enhance separation between production modes (gluon–gluon fusion [ggF], vector-boson fusion [VBF], associated production with vector bosons [$VH$], and top-associated production [$t\bar{t}H$]), neural networks (NNs) based on a Set Transformer architecture are employed. These NNs utilize global event variables and sets of reconstructed objects as inputs.
   • Framework: Results are interpreted within the Simplified Template Cross-Section (STXS) framework, specifically the "Stage-0" (production modes) and "Reduced Stage-1.2" (kinematic bins) schemes.

Key Contributions and Innovations

• Dataset: This analysis utilizes the largest dataset for this channel at 13.6 TeV (164 fb$^{-1}$), significantly improving upon previous preliminary results.
• Machine Learning: The introduction of a transformer-based (GN2) algorithm for $b$-jet identification substantially improves background rejection for the $t\bar{t}H$ production mode. Additionally, Set Transformer-based NNs are used to construct discriminants for separating production modes.
• New Observables: For the first time in this channel, a double-differential distribution of the four-lepton system transverse momentum ($p_T^{4\ell}$) as a function of the sub-leading dilepton pair invariant mass ($m_{34}$) is measured.
• Azimuthal Angle: The azimuthal angle between the two $Z$ boson decay planes ($\phi$) is reinterpreted in the context of Standard Model Effective Field Theory (SMEFT) for the first time in this channel to probe interference effects.
• Statistical Combination: A statistical combination of Run 2 and Run 3 data is performed for coupling-modifier interpretations, significantly improving constraint precision.

Results

• Inclusive Cross-Sections: The inclusive fiducial cross-section is measured to be $\sigma_{\text{fid}} = 3.65^{+0.35}_{-0.33}$ fb, consistent with the SM prediction of $3.68 \pm 0.17$ fb. The total cross-section is measured as $\sigma_{\text{total}} = 59.3 \pm 5.7$ pb, consistent with the SM value of $59.9 \pm 3.0$ pb.
• Signal Strength: The overall Higgs boson signal strength, defined as the measured cross-section normalized to the SM prediction, is $\mu = 0.99 \pm 0.13$.
• Differential Measurements: Differential cross-sections for eight observables are measured and found to be largely in agreement with SM predictions. The probability of compatibility ranges from 5% to 100% across different observables, with the $m_{12}$ distribution showing the least compatibility due to a fluctuation in the first bin.
• Production Modes: Cross-sections for ggF, VBF, $VH$, and $t\bar{t}H$ are extracted. The results are consistent with SM expectations.
• Interpretations:
  • $\kappa$-Framework: Coupling modifiers for vector bosons ($\kappa_V$) and fermions ($\kappa_f$) are constrained. The combined Run 2 and Run 3 results improve the precision on $\kappa_V$ by approximately 40% and on $\kappa_f$ by 25% compared to Run 2 alone.
  • SMEFT: Constraints are placed on CP-even and CP-odd dimension-six operators. The results are consistent with SM expectations.
  • Self-Coupling: Limits on the trilinear Higgs self-coupling modifier ($\kappa_\lambda$) are derived using both differential $p_T^{4\ell}$ and STXS measurements, yielding 95% CL intervals of $[-8.8, 19.9]$ and $[-9.0, 20.9]$ respectively, consistent with the SM.

Significance
The paper claims that these results constitute the most comprehensive ATLAS measurements of Higgs boson production in the $H \to ZZ^* \to 4\ell$ channel at $\sqrt{s} = 13.6$ TeV. The precision achieved is comparable to that obtained using the full Run 2 dataset at 13 TeV and represents an improvement by a factor of two over the first ATLAS results at 13.6 TeV in this channel. All measurements are consistent with Standard Model expectations, providing robust constraints on anomalous couplings and effective field theory operators. The analysis demonstrates the effectiveness of advanced machine learning techniques and new kinematic observables in enhancing the sensitivity of Higgs boson property measurements.