The theoretical backdrop to this search is one of the deepest puzzles in modern physics. The Standard Model of particle physics describes the known fundamental particles and forces with astonishing precision, yet it harbors an embarrassing flaw in its description of the strong nuclear force. The theory naturally permits a term that violates charge-parity symmetry, which should endow the neutron with a measurable electric dipole moment. Experiments have searched for such a moment and found nothing, constraining the offending term to a value unnaturally close to zero — a fine-tuning spanning nearly ten orders of magnitude. The celebrated solution, proposed by Roberto Peccei and Helen Quinn in 1977 and elaborated by Frank Wilczek and Steven Weinberg, postulates a new symmetry whose spontaneous breaking gives rise to a ghostly particle called the axion. But the story does not end there: extensions of the Standard Model, including string theory and supersymmetry, predict a whole zoo of axion-like particles with masses and couplings far freer than the original QCD axion allows, making them prime targets for experimental searches across an enormous range of energies.

COMPASS, mounted on the M2 beam line of CERN’s Super Proton Synchrotron, was not built to hunt for dark matter. Its 2009 campaign fired beams of negatively charged pions and muons, each carrying a hefty 190 GeV of energy, at a thin fixed target made of nickel. The original goal was a precision measurement of the charged pion polarizability — a fundamental property describing how the pion’s internal charge distribution deforms in an electric field — through a process called Primakoff Compton scattering, in which the beam particle radiates a single photon in the intense electromagnetic field of the nucleus. A parallel run with muons, which are point-like particles with no internal structure, served as a control measurement to validate the method against the exactly calculable predictions of quantum electrodynamics. The choice of a heavy nickel target was deliberate: the electromagnetic interaction scales with the square of the nuclear charge, coherently amplifying the signal while suppressing messy hadronic background processes.

The new analysis asks a provocative question: what if, among those seemingly ordinary single photons, some were actually impostors? If ALPs exist and couple to photons, they can be produced through the same Primakoff mechanism, with the beam particle emitting a virtual photon that converts into an ALP in the nuclear field. The ALP would then decay into a pair of real photons. But here the extreme beam energy becomes decisive. An ALP in the MeV mass range produced by a 190 GeV beam carries an enormous Lorentz boost, meaning its two decay photons are hurled forward in a tightly collimated jet. The electromagnetic calorimeter ECAL2, situated roughly 34 meters downstream of the target and built from lead-glass cells 3.8 centimeters across, simply cannot resolve two photon showers that arrive almost on top of each other. The pair merges into a single reconstructed cluster — indistinguishable, at first glance, from the lone photon of ordinary Compton scattering.

Quantifying exactly when this masquerade succeeds required a careful analytical model of the detector’s response. The study identifies two distinct scenarios in which an ALP decay slips through the single-photon selection. In the first, the decay is highly asymmetric: boosted kinematics can shift one photon’s energy below the calorimeter’s 2 GeV reconstruction threshold, leaving only its energetic partner to be registered. Because the scalar ALP decays isotropically in its rest frame, the probability of such asymmetric configurations can be computed exactly. In the second scenario, both photons are detectable but geometrically merge, which happens when their transverse separation at the calorimeter face falls within a single cell. A dedicated Monte Carlo simulation of the ECAL2 grid, projecting photon pairs at characteristic separations, yielded a smooth sigmoid-shaped merging probability as a function of the dimensionless separation. On top of these factors, the analysis corrects for a further subtlety: a single photon and a photon pair suffer different amounts of material attenuation from pair conversion as they traverse the nickel target and spectrometer, a correction that mildly penalizes promptly decaying ALPs and slightly favors long-lived ones.

To turn this machinery into actual limits, the study compares the observed event yields — published by COMPASS as ratios of data to simulation as a function of the photon’s energy fraction — with theoretical predictions that now include a possible ALP contribution. A profile likelihood approach, complete with a nuisance parameter that accounts for fully correlated systematic uncertainties, then scans the plane spanned by ALP mass and its coupling to photons. For each mass, the coupling is varied until the deviation from the Standard Model hypothesis crosses the statistical threshold corresponding to 95 percent confidence. The result: couplings larger than roughly 0.1 inverse GeV are excluded for ALP masses between about 0.2 and 600 MeV, carving out a swath of parameter space that sits squarely between the territory of low-mass beam dump experiments and that of high-energy colliders.

The shape of the excluded region tells a physically rich story. At low masses, ALPs become long-lived: their decay length grows so large that most of them sail clean through the detector without decaying at all, and the signal collapses exponentially. The boundary where the decay probability drops below one percent follows a simple contour in the coupling-mass plane. At the other extreme, for masses above roughly 30 MeV, the opening angle between the decay photons grows until geometrical merging becomes hopeless — yet the asymmetric-decay channel survives, sustaining a small but nonzero acceptance. This residual effect produces a distinctive high-mass tail in the pion-beam limits, stretching sensitivity all the way up to about 600 MeV, albeit at stronger couplings. Intriguingly, the pion beam outperforms the muon beam despite comparable statistics, for a beautifully simple reason: the Standard Model bremsstrahlung background scales inversely with the square of the beam particle’s mass, so the heavier pion suppresses the background and lets any ALP deviation shine through more clearly.

The work also highlights a genuine experimental advantage over competing approaches. Photoproduction experiments such as PrimEx and GlueX rely on real photon beams, which makes spotting merged diphoton signatures brutally difficult — the non-interacting beam itself floods the detector with background. COMPASS, by contrast, used charged beams, and the detection of the scattered charged particle provides a clean coincidence tag for the interaction vertex, naturally suppressing beam-related backgrounds and making the single-cluster search feasible. When the original COMPASS data were published, the mass region probed here was largely unexplored; subsequent reinterpretations of LEP data have since constrained it, but the new limits stand as an independent check built on a completely different production mechanism.

Looking ahead, the framework is anything but a one-off. The same single-cluster analysis can be applied directly to the much larger COMPASS dataset collected in 2012 with an identical setup, and the method carries forward to COMPASS’s successor, the AMBER experiment, whose planned measurement of the kaon polarizability with a 100 GeV kaon beam would modify the Standard Model background in ways that open fresh territory in the ALP parameter space. Meanwhile, an ongoing COMPASS analysis of Primakoff neutral pion production, which explicitly reconstructs resolved photon pairs, could extend sensitivity to higher masses where merging is no longer a constraint. What began as a calibration dataset for pion polarizability may yet have more secrets to surrender — proof that in particle physics, yesterday’s data can illuminate tomorrow’s dark matter.

Subject of Research: Search for axion-like particles via Primakoff production using reinterpreted COMPASS beam data

Article Title: Search for axion like particles produced via the Primakoff process at COMPASS

Article References: Dehpour, M. (2026). Search for axion like particles produced via the Primakoff process at COMPASS. The European Physical Journal C, 86(9), Article 1033. https://doi.org/10.1140/epjc/s10052-026-16296-6

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16296-6

Keywords: axion-like particles, dark matter, COMPASS experiment, CERN, Primakoff process, particle physics, photon coupling, electromagnetic calorimeter, pion polarizability, beam dump experiments, AMBER experiment, Standard Model

The standard remedy for rising noise is blunt but simple. Experimenters apply a fixed energy threshold to each individual calorimeter cell, typically set a few standard deviations above the measured noise level, so that any fluctuation below that cut is discarded as spurious. The trouble is that the threshold cannot tell the difference between noise and a real, low-energy piece of an electromagnetic shower. When a photon slams into the crystal array, it deposits its energy across many neighboring cells, and the outer cells of that shower often carry only small amounts of energy. A rigid threshold discards exactly those contributions, underestimating the total energy of the particle and worsening the resolution that precision analyses depend on, from Higgs boson mass measurements to searches for new particles and detailed studies of jet substructure.

The new study, led by Suman Das Gupta and colleagues at the Saha Institute of Nuclear Physics in Kolkata, together with collaborators in France, the United States and India, proposes a data-driven alternative. Instead of judging each cell in isolation, a machine learning model looks at the full picture: the complete shape of the electrical pulse in each crystal, the spatial pattern of energy deposits across the cluster, and the correlations among neighboring cells. The researchers framed the task as a binary classification problem at the level of individual cells, asking the network to label each one as a genuine signal hit or a noise hit, and then to use that information to reconstruct the photon’s energy more faithfully than any fixed cut could.

To train and test the approach realistically, the team built a standalone Geant4 simulation of an 11 by 11 matrix of lead-tungstate crystals, each 2.2 by 2.2 square centimeters in cross section and 22 centimeters long, arranged to mimic the geometry of the barrel section of the CMS electromagnetic calorimeter. Monoenergetic electrons were fired perpendicularly into the front face of the array, and the deposited energy in each crystal was recorded and converted into digitized waveforms following the same methodology used in the current CMS detector. Each pulse was sampled at 40 megahertz, matching the LHC bunch crossing rate, and engineered with three presamples for pedestal subtraction, with the peak timed to fall at the sixth of ten retained sampling points.

The simulation then layered on the harsh realities of collider operation. Electronic noise with a root-mean-square amplitude of 150 megaelectronvolts was injected into every crystal, with correlations between time samples modeled through a covariance matrix and generated via Cholesky decomposition. On top of that came pileup: the spray of energy from dozens of unrelated proton-proton collisions overlapping in the same bunch crossing. The researchers simulated minimum-bias interactions with Pythia8 at the Run 3 collision energy of 13.6 teraelectronvolts, drawing the number of overlapping interactions per crossing from a Poisson distribution with a mean of 50, consistent with actual LHC Run 3 conditions. Contributions from fifteen preceding bunch crossings, the in-time crossing, and nine subsequent ones were all summed into each crystal’s waveform, producing readout samples that faithfully blend signal, pileup and noise.

Before the machine learning could begin, the raw waveforms were passed through the multifit algorithm, the pulse-shape fitting technique already used by CMS, which reconstructs cell energies by fitting a linear combination of known signal and pileup templates to the observed samples via nonnegative least squares. The resulting energies, together with the ten time samples of each pulse shape, the spatial coordinates of each cell, and the energy normalized to the highest-energy seed cell, formed the input features. Each event was turned into a graph, with calorimeter cells as nodes and edges connecting spatial neighbors through a k-nearest-neighbors scheme with k equal to 24, allowing the network to reason about the local geometry of the shower.

The architecture works in three stages. First, a temporal encoder built from two one-dimensional convolutional layers compresses each cell’s ten-sample waveform into a compact feature vector. These embeddings are concatenated with the cell’s position and normalized energy, and the combined node features are fed through multiple layers of a graph neural network, which propagates information between neighboring cells so that each cell’s classification is informed by its context. Finally, a small multilayer perceptron with a sigmoid output assigns each node a probability of being a genuine signal hit. The team compared four graph convolution backbones: a standard Graph Convolutional Network, a Graph Attention Network, Edge Convolution, and Dynamic Edge Convolution, all trained with a binary cross-entropy loss augmented by two physics-motivated regularization terms, one penalizing the spread of the relative energy error and another ensuring the seed cell at the shower’s center is always retained.

While all four architectures achieved nearly identical discrimination power on the signal-versus-noise task, they diverged in how well they reconstructed energy. The Graph Attention Network emerged as the clear winner, delivering the most accurate energy scale and the lowest, most uniform standard deviation of the relative energy error across the full range of photon energies from 5 to 30 gigaelectronvolts, evaluated at a pseudorapidity of 1.4, a high-pileup region of the CMS barrel chosen deliberately as a challenging scenario. The selected model contains roughly 11,300 trainable parameters, trained on a single NVIDIA Tesla V100 GPU over 1500 epochs in about eight hours, and reaches a verdict on each event in an average of just 4.38 milliseconds, fast enough to be contemplated for real reconstruction workflows.

The head-to-head comparison against the traditional method was striking. With the ML score threshold set at 0.5 and the baseline energy cut set at 150 megaelectronvolts, comparable to the simulated noise floor, the machine learning selection consistently produced better mean reconstructed photon energy, better energy resolution, and higher signal cell efficiency at every photon energy tested, a level of performance that no value of the energy cut could replicate. Visualizations of the 11 by 11 cell window around a 15 gigaelectronvolt photon show why: the simple threshold carves away the low-energy outskirts of the true shower, while the network, reading the pulse shapes and the collective pattern of deposits, keeps those cells and rejects the noise. The authors emphasize that the approach is dynamic rather than fixed, adapting to evolving detector conditions as radiation damage deepens, which makes it particularly suited to the long-term operation of calorimeters in radiation-intensive environments and could ultimately extend the physics reach of collider experiments as luminosity continues to climb.

Subject of Research: Machine learning-based noise discrimination for electromagnetic calorimeter signal reconstruction in high-radiation particle physics detectors

Article Title: Enhancing electromagnetic calorimeter signal reconstruction with machine learning-based noise discrimination

Article References: Das Gupta, S., Ghosh, S., Gazi, L., Dutta, S., Ledovskoy, A., Bhattacharya, S., & Jain, S. (2026). Enhancing electromagnetic calorimeter signal reconstruction with machine learning-based noise discrimination. The European Physical Journal C, 86(9), Article 1134. https://doi.org/10.1140/epjc/s10052-026-16346-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16346-z

Keywords: graph neural networks, electromagnetic calorimeter, CMS experiment, Large Hadron Collider, noise discrimination, energy resolution, radiation damage, pileup, Geant4 simulation, lead-tungstate crystals, pulse-shape fitting, machine learning