Search for exotic Higgs boson decays H $\to$ $\mathcal{AA}$ with $\mathcal{AA}$ $\to$ $\gamma\gamma$ in events with a semi-merged topology in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Technical Summary: Search for Exotic Higgs Boson Decays $H \to AA$ with $A \to \gamma\gamma$ in Semi-Merged Topologies

Problem and Motivation
The search for physics beyond the Standard Model (BSM) has increasingly focused on exotic Higgs boson decays, specifically the process $H \to AA$, where $A$ is a hypothetical light spin-0 particle. While previous searches have successfully covered the fully resolved regime ($m_A \gtrsim 15$ GeV) where both $A$ bosons decay into two distinct photons, and the fully merged regime ($m_A \lesssim 1$ GeV) where both $A$ bosons decay into highly collimated photon pairs reconstructed as single objects, a significant gap existed in the intermediate mass range of $1 < m_A < 15$ GeV.

In this "semi-merged" mass regime, the kinematics of the decay $H \to AA \to 4\gamma$ present a reconstruction challenge. One $A$ boson decays into two well-separated, resolved photons, while the other $A$ boson decays into a pair of photons that are either physically merged within the electromagnetic calorimeter (ECAL) or where the secondary photon falls below the standard reconstruction threshold ($p_T > 10$ GeV). Consequently, the final state appears as three photon-like objects: two resolved photons and one "merged" photon candidate. Traditional invariant mass reconstruction is impossible for the merged leg using standard object kinematics, necessitating a novel approach to directly infer the mass of the parent $A$ particle from the calorimeter energy deposit patterns.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$ (2016–2018).

• Event Selection: Events are triggered on a diphoton system with an invariant mass $> 55$ GeV. The selection requires exactly three reconstructed photon candidates in the barrel region of the ECAL ($|\eta| < 1.44$). The two highest-$p_T$ photons must satisfy $p_T > 30$ GeV and $18$ GeV, respectively. The triphoton invariant mass ($m_{\Gamma\Gamma\Gamma}$) is constrained to the window $90 < m_{\Gamma\Gamma\Gamma} < 180$ GeV to encompass the Higgs boson signal.
• Topology Classification: The three photons are grouped into two candidates: a "resolved" candidate ($A_2$) formed by the two closest photons, and a "merged" candidate ($A_1$) formed by the third photon.
• Mass Regression via Graph Neural Networks (GNN): To reconstruct the mass of the merged candidate ($m_{A1}$), the analysis employs an end-to-end deep learning technique. Unlike previous approaches using Convolutional Neural Networks (CNNs), this analysis utilizes a Graph Neural Network (specifically a Dynamic Reduction Network).
  • Input: The input consists of a $128 \times 128$ matrix of ECAL crystal energy deposits surrounding the seed crystal of the merged candidate. The input features include transverse ($E_T$) and longitudinal ($E_z$) energy components, as well as crystal position coordinates ($x, y, z$).
  • Architecture: The network uses EdgeConv modules to dynamically construct graphs based on learned feature spaces, utilizing permutation invariance to handle the unordered nature of crystal deposits. Residual connections and pooling layers progressively reduce the graph size to a single output node predicting the mass.
  • Training and Calibration: The model is trained on simulated $A \to \gamma\gamma$ samples with flat distributions in mass and $p_T$. To handle boundary effects and distinguish signal from background (single photons), the training set includes single-photon samples assigned negative target masses ("domain continuation"). The regression response is calibrated using $Z \to e^+e^-$ events, where electrons serve as a proxy for merged photon showers, with corrections applied for scale and resolution differences between data and simulation.
• Signal and Background Modeling:
  • Signal: A 2D template of the reconstructed masses ($m_{A1}$ vs. $m_{A2}$) is constructed from simulated signal events at discrete mass points ($m_A = 1, 3, 5, 10, 15$ GeV). Intermediate masses are interpolated.
  • Background: The background model is derived entirely from data using sideband regions in both the triphoton mass ($m_{\Gamma\Gamma\Gamma}$) and the 2D mass plane. The background shape in the signal region is estimated as a linear combination of shapes from low and high $m_{\Gamma\Gamma\Gamma}$ sidebands, normalized using off-diagonal regions of the 2D mass plane to avoid signal contamination.

Key Contributions

1. Novel Reconstruction Technique: The paper introduces the application of a Graph Neural Network for mass regression of semi-merged diphoton candidates in the CMS detector. This approach leverages the full granularity of the ECAL energy deposits, outperforming traditional CNNs by naturally handling rotational symmetries and sparse data structures.
2. Bridging the Mass Gap: This analysis successfully targets the $1 < m_A < 15$ GeV mass range, a region previously inaccessible to CMS searches due to the limitations of fully resolved or fully merged topologies.
3. Data-Driven Background Estimation: The methodology employs a robust, fully data-driven background estimation strategy using 2D sidebands, minimizing reliance on simulated background processes which are difficult to model accurately for QCD multijet and $\gamma$+jet events in this specific topology.

Results
The analysis finds no statistically significant excess of events over the Standard Model background expectation in the explored mass range. Consequently, upper limits are set on the product of the Higgs boson production cross section and the branching fraction, $\sigma(pp \to H) \times \mathcal{B}(H \to AA \to 4\gamma)$, at the 95% confidence level (CL).

• Limits: The observed upper limits range from 0.264 pb at $m_A = 1$ GeV to 0.005 pb at $m_A = 15$ GeV.
• Comparison: These results represent the most stringent limits to date in the $1–5$ GeV mass range. Specifically, at $m_A = 3$ GeV, the observed limit is approximately 100 times more stringent than previous ATLAS results. The sensitivity is slightly reduced at the lowest masses compared to the fully merged CMS search (due to the dominance of the fully merged topology there) and at the highest masses (due to lower event yields and larger background uncertainties), but the semi-merged approach provides a continuous coverage across the entire spectrum.

Significance
The paper claims that this search provides the first measurement from the CMS experiment in the $m_A = 1–15$ GeV range for the $H \to AA \to 4\gamma$ channel. By developing and validating a deep learning-based mass regression technique, the analysis demonstrates the feasibility of probing exotic Higgs decays in topologies where standard reconstruction fails. The results significantly constrain BSM models involving light pseudoscalars, such as Two-Higgs-Doublet Models plus a singlet (2HDM+S) and axion-like particle production scenarios, particularly in the low-mass region where previous limits were weaker. The work establishes a new benchmark for searching for semi-merged signatures in high-energy physics.