Combination of measurements of CP properties of Higgs boson interactions with vector bosons using proton-proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data from the ATLAS detector, this paper presents a combined analysis of Higgs boson interactions with vector bosons across multiple decay channels, finding no evidence of CP violation and establishing the most stringent constraints to date on relevant CP-violating SMEFT Wilson coefficients, including simultaneous limits on three coefficients for the first time.

The Gist

The Big Picture: Hunting for a "Ghost" in the Machine

Imagine the universe as a giant, perfectly balanced seesaw. For decades, physicists have known that this seesaw is tilted. There is more matter than antimatter, and we don't know why. If the universe were perfectly symmetrical, matter and antimatter would have annihilated each other instantly after the Big Bang, leaving nothing but empty space.

To explain why we exist, there must be a "rule-breaker" in the laws of physics—a phenomenon called CP Violation (Charge-Parity violation). It's like finding a rule in a game of chess that says, "Sometimes, the white pieces can move slightly differently than the black pieces, even though the rules say they should be identical."

The Standard Model (our current rulebook for physics) has a tiny, weak rule-breaker, but it's not strong enough to explain our existence. We need a bigger, stronger rule-breaker. The Higgs boson (the particle that gives other particles mass) is the perfect place to look for this new physics.

The Experiment: The Ultimate "Shape" Detective

The ATLAS experiment at CERN is like a massive, ultra-sensitive camera taking pictures of collisions between protons (the building blocks of atoms) moving at nearly the speed of light. In this paper, the team looked at 140 "years" worth of data (140 inverse femtobarns) from these collisions.

They weren't just looking for what particles were created; they were looking at how they were created. Specifically, they were checking the shape of the Higgs boson's interactions with force-carrying particles (like the W and Z bosons).

The Analogy: The Spinning Top

Think of the Higgs boson as a spinning top.

• The Standard Model predicts the top spins perfectly upright. It's a "CP-even" object.
• New Physics might make the top wobble or tilt slightly to the left or right. This wobble is the "CP-odd" signal we are looking for.

If the top wobbles, it means the universe has a hidden "handedness" or asymmetry that we haven't seen before.

The Method: The "Optimal Observable" and the "Shape-Only" Trick

The scientists used a clever mathematical tool called the Optimal Observable. Imagine you are trying to detect if a coin is slightly weighted on one side. You don't just flip it once; you flip it a million times and look at the pattern of heads and tails.

In this experiment, they didn't care about how many Higgs bosons they found (the total number). They only cared about the shape of the data distribution.

• The Trick: They treated the total number of Higgs bosons as a "free variable." This means they said, "We don't care if the Higgs is produced 10% more or 10% less often; we only care if the pattern of its decay looks like a perfect mirror or a twisted mirror."
• Why? This isolates the "wobble" (CP violation) from other messy effects that might just change the total number of particles. It's like ignoring the volume of a song and only listening to the melody to see if it's out of tune.

The Channels: Five Different Ways to Look

To get the best picture, they combined five different "cameras" (decay channels):

1. H → γγ (Two Photons): Like seeing a flash of light.
2. H → ττ (Two Tau particles): Heavy cousins of electrons.
3. H → WW and H → ZZ:** The Higgs decaying into pairs of force-carrying particles.
4. WH (Higgs with a W boson): A specific production method where the Higgs is born alongside a W boson.

By combining all these, they created a "super-sensor" that is much more sensitive than any single camera could be alone.

The Results: The Top is Still Standing Straight

After analyzing all the data, the result was clear: The top is not wobbling.

• No Ghost Found: They found no evidence of CP violation in the Higgs boson's interactions with these force-carrying particles. The Higgs behaves exactly as the Standard Model predicts: it is a perfect, CP-even scalar.
• Tighter Constraints: While they didn't find the "ghost," they did something very important. They put the "ghost" in a very small cage. They proved that if this rule-breaking effect does exist, it is incredibly tiny—more than 40% smaller than our previous best guesses.
• Simultaneous Constraints: For the first time, they tested three different potential "rule-breakers" at the same time, rather than just one. This is like checking if a car has a flat tire, a broken engine, and a loose wheel all at once, rather than checking them one by one.

The Conclusion: A Clean Bill of Health (For Now)

This paper is a victory for precision. It tells us that the Higgs boson is a very obedient particle. It follows the Standard Model rules perfectly.

However, in science, "not finding the answer" is still a huge step forward. By ruling out large areas of "new physics," the scientists have narrowed the search. If the universe's matter-antimatter imbalance is caused by a CP-violating Higgs, it must be hiding in a very small, very subtle corner that our current tools can barely see.

In a Nutshell:
The ATLAS team took a massive snapshot of the universe's most fundamental particle, the Higgs boson, using five different angles. They looked for a subtle "tilt" that would explain why we exist. They found no tilt. The Higgs is perfectly symmetrical. But by proving it's so symmetrical, they have tightened the noose around the few remaining possibilities for new physics, guiding future experiments on where to look next.

Technical Summary

1. Problem Statement

The Standard Model (SM) of particle physics cannot explain the observed baryon asymmetry of the universe. A necessary condition for generating this asymmetry is the violation of Charge-Parity (CP) symmetry. While the SM contains CP violation via the quark mixing matrix, it is insufficient to account for the observed asymmetry. Therefore, new sources of CP violation from Beyond-the-Standard-Model (BSM) physics are required.

The Higgs boson ($H$), discovered in 2012, is predicted by the SM to be a CP-even scalar. Any deviation from this prediction, specifically CP-violating interactions between the Higgs boson and electroweak gauge bosons ($HVV$, where $V=W^\pm, Z$), would constitute a clear sign of new physics. Previous individual measurements by ATLAS and CMS have been consistent with the SM but have not fully excluded CP-violating interactions. This paper addresses the need for a global combination of these measurements to improve sensitivity and constrain the parameter space of CP-violating operators more rigorously.

2. Methodology

Data and Framework:

• Dataset: The analysis uses $140 \text{ fb}^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV, recorded by the ATLAS detector during LHC Run 2 (2015–2018).
• Theoretical Framework: The study employs the Standard Model Effective Field Theory (SMEFT) formalism. CP-violating interactions are parameterized by dimension-6 operators in the Warsaw basis. The relevant Wilson coefficients for $HVV$ interactions are:
  • $c_{\tilde{W}}$ (associated with $SU(2)_L$)
  • $c_{\tilde{B}}$ (associated with $U(1)_Y$)
  • $c_{\tilde{W}B}$ (mixed term)
• Cross-Section Decomposition: The cross-section is modeled as a sum of the SM contribution, a linear term (interference between SM and BSM, $\propto c_i/\Lambda^2$), and a quadratic term (pure BSM, $\propto c_i^2/\Lambda^4$). The analysis considers both "linear-only" and "linear + quadratic" scenarios.

Input Channels:
The combination integrates results from five distinct channels, utilizing different production and decay modes:

1. $H \to \gamma\gamma$: Vector Boson Fusion (VBF) production.
2. $H \to \tau\tau$: VBF production.
3. $H \to WW^*$: Gluon-gluon fusion (ggF) and VBF.
4. $H \to ZZ^*$: VBF and inclusive production.
5. $WH, H \to b\bar{b}$: Associated production (new measurement in this combination).

Analysis Techniques:

• CP-Odd Observables: All analyses utilize CP-odd observables (e.g., Optimal Observables (OO) for fully reconstructed decays, and angular differences like $\Delta\phi_{jj}$ or $Q_\ell \cos \delta_+$ for partial reconstruction). Under CP conservation, the average of these observables is zero.
• Shape-Only Approach: The analyses focus on the shape of the CP-sensitive distributions rather than the total normalization. Signal normalizations are treated as free floating parameters to decouple the measurement from CP-even cross-section changes.
• Statistical Combination: A combined likelihood is constructed as the product of individual channel likelihoods. Systematic uncertainties (luminosity, object reconstruction) are treated as fully correlated across channels, while background modeling uncertainties are treated as uncorrelated.
• Fit Scenarios:
  • Single-Parameter Fit: Constraining $c_{\tilde{W}}$ while fixing $c_{\tilde{B}} = c_{\tilde{W}B} = 0$.
  • Simultaneous Fit: Constraining all three coefficients ($c_{\tilde{W}}, c_{\tilde{B}}, c_{\tilde{W}B}$) simultaneously.

3. Key Contributions

• First Simultaneous Constraints: This work presents the first simultaneous constraints on the three CP-violating Wilson coefficients ($c_{\tilde{W}}, c_{\tilde{B}}, c_{\tilde{W}B}$) in the SMEFT Warsaw basis using ATLAS data.
• Inclusion of $WH, H \to b\bar{b}$: It incorporates a new, previously unpublished analysis of associated $WH$ production with Higgs decay to bottom quarks, utilizing angular observables sensitive to CP structure.
• Improved Sensitivity: By combining five channels, the analysis achieves a significant improvement in sensitivity compared to individual channel results.
• Validation of EFT Truncation: The compatibility between the "linear-only" and "linear + quadratic" fit results provides a test of the validity of truncating the SMEFT expansion at dimension-6.

4. Results

No Evidence of CP Violation:
The combined analysis finds no significant deviation from the Standard Model prediction. The best-fit values for all Wilson coefficients are consistent with zero.

Constraints on $c_{\tilde{W}}$ (Single-Parameter Fit):
At a new physics scale $\Lambda = 1$ TeV, the observed 95% Confidence Level (CL) intervals are:

• Linear-only scenario: $[-0.14, 0.49]$
• Linear + Quadratic scenario: $[-0.13, 0.60]$
• Improvement: These limits represent an improvement of over 40% compared to the previous best individual channel limits (primarily driven by the $H \to \tau\tau$ channel).

Simultaneous Fit Results:

• The simultaneous fit yields broader confidence intervals due to negative correlations between $c_{\tilde{W}}$ and the other coefficients ($c_{\tilde{B}}$ and $c_{\tilde{W}B}$).
• A large correlation is observed between $c_{\tilde{B}}$ and $c_{\tilde{W}B}$ due to similar effects on CP-odd observables in $H \to ZZ^*$, $H \to WW^*$, and $H \to \tau\tau$ channels.
• The $WH, H \to b\bar{b}$ channel is found to be independent of $c_{\tilde{B}}$ and $c_{\tilde{W}B}$ in the simultaneous fit, providing unique sensitivity to $c_{\tilde{W}}$.

Quadratic Term Effects:
In the linear + quadratic scenario, the inclusion of quadratic terms leads to a loss of sensitivity at higher Wilson coefficient values for certain channels (notably $WH, H \to b\bar{b}$), resulting in non-parabolic likelihood scans and, in some cases, undefined confidence intervals for specific regions. However, the observed 95% CL contours remain within the region where the EFT expansion is valid.

5. Significance

• Most Stringent Constraints to Date: These results provide the most stringent constraints to date on CP-violating operators in the $HVV$ sector within the SMEFT framework, with minimal model dependence.
• Comprehensive BSM Search: By combining multiple production modes (VBF, ggF, $WH$) and decay channels, the analysis covers a broad phase space, reducing the risk of missing CP-violating effects that might be hidden in a single channel.
• Foundation for Future Physics: The methodology and results set a benchmark for future analyses at the High-Luminosity LHC (HL-LHC). The ability to simultaneously constrain multiple Wilson coefficients is crucial for disentangling specific BSM models that predict specific patterns of CP violation.
• Cosmological Implications: While no CP violation was found, the tightened constraints significantly narrow the parameter space for models attempting to explain the baryon asymmetry of the universe via Higgs-sector CP violation.