Probing the Higgs-top Yukawa interaction in the $t\bar{t}H$ and $tH$ processes using $H\rightarrow\gamma\gamma$ with the ATLAS detector

Using 164 fb$^{-1}$ of 13.6 TeV proton-proton collision data collected by the ATLAS detector, this study measures the $t\bar{t}H$ cross section, sets the most stringent single-measurement upper limit on $tH$ production, and provides the most direct constraints to date on the CP structure of the Higgs-top Yukawa interaction by excluding a purely CP-odd coupling at 5.8 standard deviations.

The Gist

Imagine the universe is built like a giant, complex Lego set. For decades, scientists have been trying to figure out how the pieces snap together. In 2012, they found the most important piece of all: the Higgs boson. Think of the Higgs boson as the "glue" that gives other particles their weight (mass). Without it, the universe would be a chaotic soup of massless particles flying around at the speed of light, unable to form stars, planets, or people.

But there's a mystery. The glue doesn't just stick to everything equally. It sticks hardest to the heaviest particle, the top quark. This relationship is called the "Higgs–top Yukawa interaction."

This paper is a report from the ATLAS experiment at CERN's Large Hadron Collider (LHC). The scientists acted like cosmic detectives, smashing protons together at record-breaking speeds to recreate the conditions of the early universe. They were looking for a very specific, rare event: a collision that produces a Higgs boson along with top quarks.

Here is the breakdown of their investigation in simple terms:

1. The Detective Work: Finding a Needle in a Haystack

The scientists collected a massive amount of data (164 "inverse femtobarns," which is a fancy way of saying they watched trillions of collisions). They were looking for a specific "signature": a Higgs boson that immediately decays into two high-energy flashes of light (photons).

• The Analogy: Imagine trying to find a specific, rare firework in a stadium full of people cheering. Most of the time, you just see a sea of noise (background noise). But sometimes, two specific people light up a distinct, bright spark. The scientists built a super-smart computer filter (using something called a Graph Neural Network) to ignore the cheering crowd and focus only on those two bright sparks.

2. The Two Ways to Catch the Glue

The Higgs boson can be produced with top quarks in two main ways:

1. The "Double Trouble" ($t\bar{t}H$): The collision creates a pair of top quarks and a Higgs boson. This is like finding two heavy anchors and a piece of glue together.
2. The "Single Rider" ($tH$): The collision creates just one top quark and a Higgs boson. This is much rarer and harder to spot, like finding a single anchor and a piece of glue in a storm.

3. The Big Question: Is the Glue "Pure" or "Mixed"?

The Standard Model (our current best theory of physics) says the glue is "pure." It behaves in a specific, predictable way (called "CP-even"). However, some theories suggest the glue might be "mixed" with a hidden, strange property (called "CP-odd"). If the glue is mixed, it could explain why the universe has more matter than antimatter.

To test this, the scientists looked at the angles and speeds of the particles.

• The Analogy: Imagine spinning a top. If it's a "pure" top, it spins one way. If it's a "mixed" top, it might wobble or spin differently. By measuring exactly how the top quarks and the Higgs boson move away from the collision point, the scientists could tell if the glue was behaving normally or if it had that "wobble."

4. The Results: What They Found

• The "Double Trouble" ($t\bar{t}H$): They found this event happening exactly as predicted. The rate was about 13% higher than the Standard Model predicted, but this is well within the margin of error (like a weather forecast saying "70% chance of rain" and it raining 80% of the time). They confirmed the glue exists and is strong.
• The "Single Rider" ($tH$): This is the rare one. They didn't see enough of these events to say for sure they found them, but they set a very strict limit. They can say with 95% confidence that this event doesn't happen more than 6.2 times the predicted rate. This is the tightest limit ever set for this specific event.
• The "Wobble" (CP Structure): This is the most important finding. They combined their new data with older data from previous years. They looked for that "wobble" in the glue.
  • The Verdict: They found no evidence of a wobble.
  • The Stat: They ruled out the possibility that the glue is "purely mixed" (purely CP-odd) with a confidence level of 5.8 standard deviations. In science, 5 standard deviations is the "gold standard" for a discovery. This means it is virtually impossible (less than a 1 in a million chance) that the glue is purely the "weird" kind. The glue is overwhelmingly "normal."

5. Why This Matters

This paper doesn't invent a new technology or cure a disease. Instead, it tightens the screws on our understanding of reality.

• It confirms that the heaviest particle in the universe interacts with the Higgs boson exactly as our best theory predicts.
• It puts a huge "No Entry" sign on the idea that the Higgs boson has a hidden, strange "mirror" property that could explain the universe's matter-antimatter imbalance.

In summary: The ATLAS team used the world's most powerful microscope to watch the universe's heaviest particles dance with the Higgs boson. They confirmed the dance steps are exactly as the "Standard Model" choreographer wrote them, and they have effectively ruled out the idea that the dance has a secret, hidden twist. The universe, at least in this regard, is behaving very predictably.

Technical Summary

Technical Summary: Probing the Higgs–top Yukawa interaction in the $t\bar{t}H$ and $tH$ processes using $H \to \gamma\gamma$ with the ATLAS detector

Problem and Motivation
The discovery of the Higgs boson and the observation of its production modes at the Large Hadron Collider (LHC) provide a unique opportunity to search for physics beyond the Standard Model (SM) by precisely characterizing Higgs boson properties. In the SM, the Higgs boson is a scalar particle ($J^{CP} = 0^{++}$). The observation of a non-zero $CP$-odd component in any Higgs interaction would constitute unambiguous evidence for new physics. While a pure pseudoscalar hypothesis has been excluded, a $CP$-mixed state remains compatible with current observations and could provide necessary sources of $CP$ violation for baryogenesis.

Measurements of the Higgs boson $CP$ structure through Yukawa interactions are particularly sensitive because fermions can couple directly to pseudoscalar states at tree level, unlike $CP$-odd contributions to Higgs–vector-boson couplings which arise only at loop level. Among these, the Higgs–top coupling is the largest in the SM, driving dominant radiative corrections to the Higgs mass, controlling the running of the Higgs quartic coupling, and offering a uniquely sensitive probe of the $CP$ structure. This paper presents a study of the Higgs–top Yukawa interaction using the associated production of the Higgs boson with a top quark pair ($t\bar{t}H$) and a single top quark ($tH$) in the diphoton ($H \to \gamma\gamma$) decay channel.

Methodology
The analysis utilizes proton–proton collision data collected by the ATLAS detector at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of $164 \text{ fb}^{-1}$ (Run 3). To maximize sensitivity, these results are combined with a previous ATLAS measurement of the same processes in the diphoton channel using $140 \text{ fb}^{-1}$ of data at $\sqrt{s} = 13$ TeV (Run 2).

• Event Selection and Reconstruction: Events are selected requiring two photon candidates passing tight identification and isolation criteria, with transverse momentum ($p_T$) requirements relative to the diphoton invariant mass ($m_{\gamma\gamma}$). The invariant mass is constrained to $m_{\gamma\gamma} \in [105, 160]$ GeV. Events must contain at least one $b$-tagged jet (using the GN2 transformer-based neural network with an 85% working point) and isolated leptons are used to categorize events into Hadronic (no isolated leptons) and Leptonic (at least one isolated lepton) topologies.
• Machine Learning Classification: A four-stage event classification strategy is employed:
  1. Preselection: Separation into Hadronic and Leptonic categories.
  2. Signal Enrichment: A multiclass Graph Neural Network (GNN) classifier separates events into $t\bar{t}H$, $tWH$, and $tHjb$ (single-top Higgs with a forward jet) enriched classes, as well as resonant and continuum background categories.
  3. $CP$ Sensitivity: A binary GNN classifier discriminates between $CP$-even-like and $CP$-odd-like signal topologies. This classifier is trained on simulation with positive mixing angles ($\alpha$) and is sensitive to kinematic features such as jet $p_T$, photon $\eta$ and $\phi$, and missing transverse energy correlations.
  4. Background Purity: Final categories are subdivided based on background probabilities to maximize signal sensitivity.
     This strategy results in 32 distinct event categories.
• Statistical Analysis: A likelihood function is constructed from the diphoton invariant mass distributions in the 32 categories. Signal and background shapes are parameterized using power laws, exponentials, and double-sided Crystal Ball functions. Systematic uncertainties (theoretical, experimental, and background modeling) are treated as nuisance parameters. The $CP$-mixing angle $\alpha$ and coupling strength $\kappa_t$ are parameterized in the Higgs Characterization model. The analysis combines Run 3 data with Run 2 data, correlating nuisance parameters of shared origin.

Key Contributions and Results

• $t\bar{t}H$ Cross Section Measurement: Assuming a purely $CP$-even coupling, the observed signal strength for the $t\bar{t}H$ process is $\mu_{t\bar{t}H} = 1.13^{+0.33}_{-0.28}$, corresponding to a cross section times branching ratio of $\sigma_{t\bar{t}H} \times \mathcal{B}_{\gamma\gamma} = 1.46^{+0.40}_{-0.35}$ fb at $\sqrt{s} = 13.6$ TeV. This represents a $5.0\sigma$ observation of the $t\bar{t}H$ process in this channel.
• $tH$ Cross Section Limit: The signal strength for the $tH$ process is measured to be $\mu_{tH} = 1.70^{+2.32}_{-1.93}$. An observed 95% confidence level (CL) upper limit on the $tH$ production cross section is set at 6.2 times the SM prediction, compared to an expected limit of 4.4. This constitutes the most stringent $tH$ upper limit achieved in a single measurement to date.
• $CP$-Mixing Angle Constraints:
  • Run 3 Only: Using the Run 3 dataset, values of the $CP$-mixing angle $|\alpha| > 53^\circ$ are excluded at 95% CL. A purely $CP$-odd scenario ($\alpha = 90^\circ$) is rejected with a significance of $4.2\sigma$.
  • Combined Run 2 + Run 3: The statistical combination yields the most stringent direct constraints on the $CP$ structure of the Higgs–top Yukawa interaction to date. The observed 95% CL exclusion is $|\alpha| > 38^\circ$ (expected $48^\circ$). A purely $CP$-odd Higgs-top Yukawa coupling is excluded at the level of $5.8\sigma$ (expected $4.7\sigma$).
• Coupling Strength: Assuming a $CP$-even coupling, the top Yukawa coupling parameter is measured to be $\kappa_t = 1.11^{+0.11}_{-0.11}$ in the combined analysis.

Significance
The paper claims that this analysis provides the most stringent direct constraints on the $CP$ structure of the Higgs–top Yukawa interaction to date. The improvement in sensitivity compared to previous Run 2 analyses (a 55% increase in exclusion significance for $\alpha = 45^\circ$ and $90^\circ$) is driven primarily by the updated analysis strategy, specifically the use of GNN-based categorization which reduces the correlation between $t\bar{t}H$ and $tH$ rate measurements from $-44\%$ to $-28\%$ and better isolates $CP$-dependent kinematic features. The exclusion of a purely $CP$-odd coupling at $5.8\sigma$ represents a major step in characterizing the Higgs sector and constraining potential sources of $CP$ violation relevant to baryogenesis.