Search for the Higgs boson decay to a $Z$ boson and a photon in $pp$ collisions at $\sqrt{s}=13$ TeV and $13.6$ TeV with the ATLAS detector

Using 165 fb$^{-1}$ of 13.6 TeV proton-proton collision data recorded by the ATLAS detector and combining it with previous 13 TeV results, this study performs a search for the rare Higgs boson decay to a $Z$ boson and a photon, finding a signal strength consistent with the Standard Model expectation with an observed significance of 2.5 standard deviations.

The Gist

The Big Picture: Hunting for a Ghostly Whisper

Imagine the Higgs boson as a very shy celebrity who usually hangs out with a massive crowd of other particles. For years, scientists have watched this celebrity interact with almost everyone they know. But there is one specific interaction that has been incredibly hard to catch: the Higgs boson saying goodbye to a Z boson (a heavy particle) while simultaneously flashing a photon (a particle of light).

This paper is a report from the ATLAS experiment at the Large Hadron Collider (LHC). It's like a team of super-sleuths trying to find a specific, rare fingerprint in a massive pile of mud. They are looking for the moment the Higgs boson decays into a Z boson and a photon ($H \to Z\gamma$).

The Setup: A High-Speed Collision Factory

To find this rare event, the scientists smashed protons together at record-breaking speeds (13.6 TeV). Think of this as firing two cars at each other at 99.9% the speed of light. When they crash, they explode into a shower of new particles.

• The Data: They collected data from 2022 to 2024, which is like having a library of 165 "petabytes" of collision stories.
• The Goal: They wanted to see if the Higgs boson behaves exactly as the "Standard Model" (the rulebook of physics) predicts, or if it's doing something weird that hints at new, unknown physics.

The Detective Work: Sorting the Noise

The problem is that for every time the Higgs boson does this special dance, there are millions of other collisions that look similar but are just background noise. It's like trying to hear a single person whispering your name in a stadium full of people cheering.

To solve this, the ATLAS team used a clever sorting strategy:

1. The "Lepton" Filter: They looked for specific pairs of electrons or muons (lightweight cousins of electrons) that come from the Z boson.
2. The "Photon" Flash: They looked for a high-energy flash of light (the photon).
3. The "XGBoost" Brain: Instead of just using simple rules, they trained a sophisticated computer algorithm (like a highly experienced detective) to look at the shape and energy of the crash. This algorithm sorts the events into 13 different categories.
   • Some categories look for crashes where the Higgs was made alongside other heavy particles (like top quarks).
   • Others look for crashes where the Higgs was made by smashing two "gluons" together.
   • By splitting the data into these 13 groups, they could tune their search to be extra sensitive in each specific type of crash.

The Findings: A Nod, Not a Shout

After analyzing all the data, here is what they found:

• The Signal: They saw a small bump in the data where the Higgs boson should be. It's like hearing a faint whisper in the crowd.
• The Match: The number of times they saw this event matches the Standard Model's prediction almost perfectly.
  • If the Standard Model predicted 100 events, they saw about 90 to 130 (give or take).
  • The "signal strength" (a number representing how strong the signal is compared to the prediction) is 1.3 when combining this new data with older data from 2015–2018.
• The Significance: In the world of particle physics, "significance" is measured in "sigmas" ($\sigma$).
  • A 3-sigma result is considered "evidence" (a strong hint).
  • A 5-sigma result is a "discovery" (a shout).
  • This result is about 2.5 sigma. This means it's a very promising hint, but not quite a definitive discovery yet. It's like seeing a shadow that looks exactly like a ghost, but you need more light to be 100% sure it's not just a coat rack.

The Conclusion: The Rulebook Still Holds

The main takeaway is that the Higgs boson is behaving exactly as the rulebook says it should.

• No Surprises: They didn't find any "new physics" (like hidden particles or strange forces) altering the rate of this decay.
• Consistency: The result is consistent with previous measurements from the CMS experiment and earlier ATLAS runs.
• The Future: While they haven't found a new particle, they have tightened the net. By combining their new data with old data, they have the most sensitive search for this specific decay ever performed. If the Higgs boson is hiding a secret, it's going to be very hard to find.

In short: The ATLAS team looked for a rare, ghostly interaction between the Higgs boson, a Z boson, and a photon. They found a faint signal that matches the predictions of our current understanding of the universe perfectly. The universe, for now, is behaving exactly as expected.

Technical Summary

Technical Summary: Search for the Higgs boson decay to a $Z$ boson and a photon in $pp$ collisions at $\sqrt{s}=13$ TeV and 13.6 TeV with the ATLAS detector

Problem and Motivation
The Standard Model (SM) predicts that the Higgs boson ($H$) decays to a $Z$ boson and a photon ($H \to Z\gamma$) via loop-induced processes, with a branching ratio of approximately $1.54 \times 10^{-3}$ for a Higgs mass of 125.09 GeV. While the $H \to \gamma\gamma$ and $H \to ZZ^*$ decays have been well-established, the $H \to Z\gamma$ channel remains a critical, yet experimentally challenging, probe. As a loop-induced process, its rate is sensitive to contributions from new physics particles (such as additional scalars, fermions, or vector bosons) circulating in the loops, which could alter the branching ratio relative to SM predictions. Furthermore, observing this decay completes the suite of Higgs decays into pairs of electroweak gauge bosons, solidifying the understanding of electroweak symmetry breaking. Previous searches by ATLAS and CMS using Run-2 data ($\sqrt{s}=13$ TeV) provided the first evidence of this decay with a combined significance of $3.4\sigma$, but with large uncertainties. This paper presents an updated search utilizing the higher-energy Run-3 dataset and combining it with Run-2 results to improve sensitivity.

Methodology
The analysis utilizes proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider (LHC).

• Datasets: The primary dataset corresponds to $\sqrt{s}=13.6$ TeV collisions collected during 2022–2024 (Run 3), with an integrated luminosity of 165 fb$^{-1}$. This is combined with the previous Run-2 dataset ($\sqrt{s}=13$ TeV, 140 fb$^{-1}$).
• Final State: The search targets the $H \to Z(\to \ell\ell)\gamma$ decay, where $\ell = e$ or $\mu$. This channel is selected for its clean signature, full kinematic reconstruction, and excellent invariant mass resolution, despite a reduced branching ratio compared to other modes.
• Event Selection and Reconstruction:
  • Events are triggered using single- and dilepton triggers with relaxed $p_T$ thresholds compared to Run-2 (e.g., single-muon $p_T > 24$ GeV).
  • Offline selection requires one photon and two same-flavour, opposite-charge leptons associated with the primary vertex.
  • Photon identification is tightened, but the $p_T$ threshold is lowered to 10 GeV (from 15 GeV in Run-2) to enhance efficiency, relying on improved calibration.
  • A kinematic fit constrains the dilepton mass to the known $Z$ boson mass, improving the $Z\gamma$ invariant mass ($m_{Z\gamma}$) resolution by 17% for electrons and 11% for muons.
• Event Categorization: To maximize sensitivity, events are classified into 13 mutually exclusive categories based on kinematic properties and production modes:
  • Lepton Category: Events with $\ge 3$ leptons, enriched in $VH$ and $t\bar{t}H$ production.
  • VBF Region: Events with $\ge 2$ jets, split into Tight (VBFT) and Loose (VBFL) categories using an XGBoost-based multivariate classifier.
  • Relative Photon $p_T$ Regions: Events are split into High ($p_T^\gamma/m_{Z\gamma} \ge 0.4$) and Low ($< 0.4$) relative photon $p_T$ regions. These are further subdivided by lepton flavour ($e$ or $\mu$) and BDT score (Tight, Medium, Loose).
  • This strategy replaces the previous rectangular selection approach with a multivariate classifier (XGBoost) to better separate signal from the dominant non-resonant $Z\gamma$ and $Z$+jets backgrounds.
• Signal and Background Modelling:
  • The signal shape is modelled by a double-sided Crystal Ball (DSCB) function.
  • Backgrounds are dominated by non-resonant $Z\gamma$ production and $Z$+jets (where a jet fakes a photon). The $Z$+jets fraction is estimated using a data-driven sideband method.
  • A simultaneous unbinned extended maximum-likelihood fit is performed on the $m_{Z\gamma}$ spectrum across all categories.
  • Systematic uncertainties, including those from background modelling (spurious signal), luminosity, and theoretical cross-sections, are incorporated as nuisance parameters.

Key Contributions

1. Run-3 Analysis: This work presents the first ATLAS search for $H \to Z\gamma$ using Run-3 data at $\sqrt{s}=13.6$ TeV.
2. Optimized Categorization: The introduction of a dedicated multi-lepton category targeting $VH$ and $t\bar{t}H$ production, alongside the use of XGBoost classifiers for the remaining categories, represents a significant methodological upgrade over the Run-2 analysis.
3. Combined Sensitivity: The paper provides the most stringent expected sensitivity to date for this rare decay by combining the Run-3 results with the Run-2 measurement.

Results

• Run-3 Only: For the 165 fb$^{-1}$ dataset at 13.6 TeV, the measured signal strength relative to the SM prediction is $\mu = 0.9^{+0.7}_{-0.6}$. The observed significance is 1.4$\sigma$ (expected 1.5$\sigma$). The result is consistent with the SM expectation.
• Combined Run-2 and Run-3: The combination yields an observed signal strength of $\mu = 1.3^{+0.6}_{-0.5}$ (expected $\mu = 1.0^{+0.6}_{-0.5}$).
• Significance: The combined analysis achieves an observed significance of 2.5$\sigma$ (expected 1.9$\sigma$) for the signal hypothesis over the background-only hypothesis.
• Branching Ratio: Assuming SM production cross-sections, the observed branching fraction is $(2.0^{+0.9}_{-0.8}) \times 10^{-3}$, consistent with the SM prediction of $(1.54^{+0.10}_{-0.11}) \times 10^{-3}$.
• Improvement: The expected significance of the combined result improves by 61% relative to the Run-2 measurement alone. The Run-3 analysis alone shows a 28% improvement in expected significance over the previous Run-2 result, driven by 15% from enhanced selection/categorisation and the remainder from increased luminosity and cross-section.

Significance and Claims
The paper claims that this measurement represents the most stringent expected sensitivity to the $H \to Z\gamma$ decay to date, surpassing the previous ATLAS + CMS Run-2 combination. The results are fully consistent with the Standard Model, showing no significant deviation in the Higgs boson's behaviour in the $Z\gamma$ channel. The analysis demonstrates the effectiveness of the Run-3 detector performance and advanced multivariate techniques in probing rare Higgs decays. The authors conclude that while the current data does not provide evidence for new physics, the improved precision sets tighter constraints on models predicting deviations in the $H \to Z\gamma$ rate.