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Search for the rare Higgs boson decay H $\to$ Z $\gamma$ in proton-proton collisions at $\sqrt{s}$ = 13 and 13.6 TeV

The CMS experiment analyzed 200 fb $^{-1}$ of proton-proton collision data at 13 and 13.6 TeV to search for the rare Higgs boson decay $H \to Z\gamma$ , observing a signal strength consistent with the Standard Model prediction with an observed significance of 1.9 standard deviations.

Original authors: CMS Collaboration

Published 2026-09-07

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CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, invisible architecture of the universe, there exists a fundamental field that gives mass to the particles that make up everything we see. Without this field, the building blocks of matter would zip around at the speed of light, unable to clump together to form atoms, stars, or people. The particle associated with this field is the Higgs boson, a discovery made in 2012 that confirmed a decades-old theory about how the universe works. Since that discovery, physicists have been busy measuring the properties of this particle with extreme precision, checking if it behaves exactly as the standard model of physics predicts or if it shows tiny cracks that might lead to new, unknown laws of nature. One of the most difficult ways to test this is by watching the Higgs boson decay, or break apart, into other particles. While it usually breaks into common particles, it is also predicted to occasionally transform into a Z boson and a photon of light. This specific transformation is extremely rare, happening only about once in every thousand decays, making it a needle-in-a-haystack search that requires immense amounts of data and sophisticated tools to find.

A researcher working with the CMS experiment at the Large Hadron Collider in Switzerland has just completed a massive search for this rare event. They analyzed a colossal dataset of collisions between protons, the tiny particles that make up atomic nuclei, which were smashed together at energies of 13 and 13.6 trillion electronvolts. This data, collected over several years, represents a total of 200 inverse femtobarns of luminosity, a measure of how many collisions occurred. To find the Higgs boson decaying into a Z boson and a photon, the scientist looked for a very specific signature: a pair of charged particles (either electrons or muons) coming from the Z boson, accompanied by a single, high-energy photon. Because the Z boson is unstable, it immediately breaks apart into these two charged particles, leaving a clear trail in the detector. The challenge was that the background noise from other common particle interactions is enormous, creating millions of events that look almost identical to the signal the scientist was hunting for.

To separate the signal from the noise, the researcher did not rely on a single method but instead built a complex, multi-layered strategy. They first sorted the collision events into different categories based on how the Higgs boson was likely created. Some events came from the collision of two gluons, the particles that hold atomic nuclei together, while others came from the fusion of force-carrying particles or the association with other heavy particles like top quarks. For the most common type of creation, they used advanced computer algorithms, known as boosted decision trees, to learn the subtle differences between a true signal and a background event. These algorithms analyzed dozens of characteristics, such as the angles at which particles flew apart and the energy they carried, to assign a score that indicated how likely an event was to be the rare decay they were seeking. They also applied a special mathematical technique to refine the measurement of the particles' energies, effectively sharpening the image of the data to make the signal stand out more clearly against the background.

After applying all these filters and sorting the millions of events into thirteen distinct categories, the researcher performed a simultaneous statistical analysis to look for a small excess of events at the specific mass of the Higgs boson, which is about 125.38 gigaelectronvolts. The result was a measurement of the signal strength, which compares how often they saw the event to how often the standard model says it should happen. They found a signal strength of 1.10, meaning they observed slightly more events than predicted, but the difference was small enough to be consistent with random statistical fluctuations. The statistical significance of this observation was 1.9 standard deviations, a measure of how unlikely it is that the result is just a fluke. In the world of particle physics, a discovery requires a significance of five standard deviations, so this result is not yet a confirmed discovery, but it is a meaningful step forward. The researcher also calculated what they expected to see based on their simulations, which was a significance of 2.3 standard deviations, showing that their actual results were very close to their expectations.

The study confirms that the Higgs boson behaves largely as the standard model predicts, even in this rare and difficult-to-observe decay channel. While the data showed a slight upward fluctuation, it was not large enough to claim that new physics has been found or that the standard model is wrong. The researcher carefully accounted for every possible source of error, from the calibration of their detectors to the theoretical calculations of how often these events should occur. They found that the uncertainties in their measurements were dominated by the limited amount of data available, rather than by flaws in their equipment or methods. This work represents a significant improvement over previous searches, increasing the expected sensitivity by about fifty percent through better trigger strategies, more refined event categorization, and improved machine learning techniques. By pushing the boundaries of what can be measured, the researcher has narrowed the window for potential new physics, even if they have not yet opened the door to it.

The implications of this search extend beyond just counting events. Because the decay of the Higgs boson into a Z boson and a photon happens through a loop of virtual particles, it is sensitive to any new, heavy particles that might exist but are too massive to be produced directly. If such particles existed, they would alter the rate of this decay. The fact that the observed rate matches the standard model prediction so closely suggests that there are no large, hidden contributions from unknown particles affecting this process. However, the measurement is still limited by statistics, meaning that with more data, the precision will improve, and the ability to spot tiny deviations will increase. The researcher has made their data and analysis tools available to the wider scientific community, ensuring that this result can be combined with other measurements to build an even clearer picture of the Higgs boson.

In the end, this paper is a testament to the power of patience and precision in modern science. The researcher did not find a dramatic new particle or a sudden revolution in physics, but they did successfully map out a very difficult corner of the subatomic world with greater clarity than ever before. They have shown that the Higgs boson, even in its most elusive decay modes, continues to follow the rules laid out by the standard model. The search continues, and with the Large Hadron Collider still running and collecting data, the next generation of measurements will likely push these limits even further, turning these small hints of significance into definitive answers about the fundamental nature of reality.

Technical Summary: Search for the Rare Higgs Boson Decay $H \to Z\gamma$ in Proton-Proton Collisions at $\sqrt{s} = 13$ and 13.6 TeV

Problem and Motivation
The discovery of the Higgs boson ( $H$ ) in 2012 confirmed the mechanism of electroweak symmetry breaking. However, a comprehensive program of measurements is required to test Standard Model (SM) predictions and probe for physics beyond the SM (BSM). The decay $H \to Z\gamma$ is a rare, loop-induced process with a predicted SM branching fraction of $(1.5 \pm 0.1) \times 10^{-3}$ . Unlike tree-level decays, this process proceeds only through loop diagrams dominated by $W$ bosons and, to a lesser extent, top quarks. Consequently, it is highly sensitive to contributions from BSM particles entering these loops or to scenarios where the Higgs is a composite Nambu–Goldstone boson. Previous searches by ATLAS and CMS using Run 2 data yielded statistical significances below 3 standard deviations, with a combined significance of 3.4 standard deviations. This paper presents an updated search utilizing the full Run 2 dataset (2016–2018) and the initial Run 3 dataset (2022–2023) to improve sensitivity.

Methodology
The analysis utilizes proton-proton collision data recorded by the CMS experiment at center-of-mass energies of 13 TeV (138 fb $^{-1}$ ) and 13.6 TeV (62 fb $^{-1}$ ), totaling an integrated luminosity of 200 fb $^{-1}$ . The search targets the decay chain $H \to Z\gamma$ with $Z \to \ell^+\ell^-$ ( $\ell = e, \mu$ ).

Event Selection and Reconstruction: Events are selected using single-lepton and dilepton triggers. The analysis requires two opposite-sign same-flavor leptons with an invariant mass compatible with the $Z$ boson ( $80 < m_{\ell\ell} < 100$ GeV) and an isolated photon. Kinematic requirements, such as $p_T(\gamma)/m_{\ell\ell\gamma} > 15/110$ and $m_{\ell\ell\gamma} + m_{\ell\ell} > 185$ GeV, are applied to suppress non-resonant backgrounds, particularly $Z + \text{fake photon}$ events.
Event Categorization: To optimize sensitivity across different production mechanisms, events are assigned to 13 non-overlapping categories:
- Gluon-Gluon Fusion (ggF): Four categories defined by a Boosted Decision Tree (BDT) score, allowing at most one jet.
- Vector Boson Fusion (VBF): Four BDT-defined categories requiring at least two non-b-tagged jets.
- Associated Production (VH, ttH): Five categories targeting $ZH$ , $W^\pm H$ , and $t\bar{t}H$ production, utilizing requirements on lepton multiplicity, $b$ -tagged jets, and missing transverse momentum ( $p_T^{\text{miss}}$ ).
- Untagged: Events not fitting the above criteria.
Signal Extraction: The signal is extracted via a simultaneous maximum likelihood fit to the invariant mass distribution of the $\ell^+\ell^-\gamma$ $ℓ^{+} ℓ^{-} γ$ system ( $m_{\ell\ell\gamma}$ $m_{ℓℓ γ}$ ) across all 13 categories.
- Signal Model: Modeled by a double-sided Crystal Ball function with a Gaussian core, with parameters interpolated from simulated samples at $m_H = 120, 125, 130$ GeV to the nominal mass of 125.38 GeV.
- Background Model: Non-resonant backgrounds ( $Z\gamma$ and $Z + \text{fake photon}$ ) are modeled using empirical functions selected via a discrete profiling method to avoid bias. A small resonant background from $H \to \mu^+\mu^-\gamma$ (final-state radiation) is included and constrained to its SM yield.
- Resolution Improvement: A $Z$ -line-shape-constrained fit is performed on the lepton four-momenta to improve the $m_{\ell\ell\gamma}$ mass resolution by 10–20%.

Key Contributions and Improvements
This analysis introduces several enhancements over the previous CMS Run 2 measurement:

Expanded Dataset: Inclusion of 62 fb $^{-1}$ of Run 3 data at 13.6 TeV, increasing the total luminosity by ~45% and the production cross section by ~5%.
Trigger Strategy: Implementation of a logical OR of single-lepton and dilepton triggers, increasing efficiency by ~10%.
Categorization: A refined primary categorization scheme with additional BDT-based secondary categories for ggF and VBF, optimizing sensitivity to specific production modes.
Object Identification: Improved selection criteria and machine-learning algorithms (BDTs) for event classification, utilizing variables such as photon identification scores, angular correlations, and jet kinematics.
Systematic Treatment: A more rigorous treatment of systematic uncertainties, including the discrete profiling of background shape functions and detailed validation of signal models.

Results
The simultaneous fit to the 13 event categories yields the following results for a Higgs boson mass of 125.38 GeV:

Signal Strength ( $\mu$ ): The observed signal strength, defined as the ratio of the measured cross-section times branching fraction to the SM prediction, is $\mu = 1.10^{+0.52}_{-0.61}$ . The expected signal strength is $1.00^{+0.49}_{-0.46}$ .
Significance: The observed (expected) significance of the signal excess is 1.9 (2.3) standard deviations.
Compatibility: The $p$ -value for the compatibility of the 13 separate categories is 0.75, indicating no significant tension between categories.
Uncertainty Breakdown: The total uncertainty is dominated by statistical limitations. The systematic uncertainty is relatively small, with the largest component arising from theoretical uncertainties in fixed-order calculations (9% contribution to the signal strength uncertainty).

Significance and Claims
The paper claims that this analysis represents a significant improvement in sensitivity, with an expected significance improved by approximately 50% relative to an extrapolation of the previous CMS measurement to the same luminosity. The result is consistent with the Standard Model prediction ( $\mu = 1$ ). While the observed significance (1.9 $\sigma$ ) does not constitute an observation, the analysis provides the most stringent constraints on the $H \to Z\gamma$ decay rate to date using the combined Run 2 and Run 3 datasets. The author emphasizes that the measurement remains statistically limited, but the improved methodology and larger dataset provide a robust framework for future precision measurements as the LHC accumulates more data. The results are consistent with previous combinations but offer a more detailed breakdown of production channels and improved systematic handling.

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