A test of four ways to reconstruct particle tracks in HIBEAM found no overall winner when simulated Compton-electron backgrounds were added. TrackLess and GraphNeT kept the reconstructed interaction point tighter, while Kalman and IterGNN recovered more events. The authors describe this as a resolution-efficiency trade-off within a simulated HIBEAM topology and detector model, rather than a universally best method.
A deliberately difficult tracking test
The study examined an annihilation pattern in HIBEAM's time projection chamber, where simulated detector hits mark particle paths in three dimensions. Researchers varied the background by injecting 0, 1, 2, 4 or 8 Compton electrons into each simulated annihilation event. These electrons were assigned isotropically generated inward directions and a kinetic energy of 5 MeV.
The underlying sample contained 105 distinct simulated annihilation vertices. Randomized foil coordinates and azimuthal rotations were used for factor-of-ten oversampling, producing 106 generated signal events with a uniform distribution of true vertices. Particle transport was simulated with Geant4; hit points were sampled every 1 cm along trajectories and their coordinates were independently smeared with a Gaussian width of 0.5 mm.
Four routes to the same answer
The same simulated hit samples were processed by four reconstruction approaches. Kalman used adaptive track fitting; TrackLess combined geometric projection and clustering; GraphNeT used an open-source graph-neural-network framework; and IterGNN linked custom clustering with a graph-neural-network chain. For IterGNN, each Compton setting used 150,000 events for training, 50,000 for validation and 100,000 held out for testing.
The main score was the distance between the reconstructed and true interaction points across the target foil, measured in the transverse plane. The reconstructed z coordinate was fixed to 0, so the study assessed two-dimensional placement on the foil rather than full three-dimensional vertex resolution. Results were reported using the radius containing 50% of errors, the wider radius containing 90%, the widths of x and y errors, and the share of events with an accepted vertex.
Background changed the balance
With no injected Compton electrons, all four methods had millimetre-scale median radial errors, but their tails differed sharply. The 50% radial containments were 6.1 mm for Kalman, 4.6 mm for TrackLess, 4.3 mm for GraphNeT and 5.6 mm for IterGNN. At the 90% level, the corresponding radii were 107, 12, 15 and 28 mm. Reconstruction efficiencies were 79%, 68%, 80% and 79%, respectively.
The gap widened in the most demanding simulated sample, with 8 injected Compton electrons per event. Kalman's 50% and 90% radial containments grew to 54 mm and 244 mm. TrackLess recorded 5.4 mm and 30 mm, GraphNeT 7.0 mm and 32 mm, while IterGNN reached 8.7 mm and 116 mm. On these simulated stress tests, TrackLess and GraphNeT therefore retained tighter radial performance than Kalman, with IterGNN between them.
Efficiency moved in the opposite direction for some methods. At zero injected electrons, the reported efficiencies were 79% for Kalman, 68% for TrackLess, 80% for GraphNeT and 79% for IterGNN. At eight electrons, they were 94%, 70%, 80% and 94%. Kalman and IterGNN thus ended with the highest reported efficiencies in the most heavily injected sample, while TrackLess stayed lower and GraphNeT remained stable.
What the neural networks added
IterGNN found more than 99% of both the signal tracks and the injected Compton tracks across the tested samples. Its TrackGNN classifier, which separates track types, had a classification score measured by the area under the receiver-operating-characteristic curve of 0.72 with no injected Compton electrons and 0.96 with eight. These are point estimates from the simulations, with no confidence intervals reported.
The authors' interpretation is that machine-learning methods did not produce a universal improvement in the vertex coordinates for this geometrically simple simulated topology. Their additional outputs, including track classification, track-count estimates, vertex-uncertainty estimates and related event-shape information, add information beyond the coordinates, but the supplied analysis does not establish a benefit for a downstream physics analysis.
Nearly complete coverage came at a cost
The main analysis required at least two tracks. When otherwise-rejected single-track events were kept, efficiency at zero injected electrons rose to 97%, 97%, 98% and 97% for Kalman, TrackLess, GraphNeT and IterGNN. At eight injected electrons, it reached 99%, 100%, 100% and 100%. The associated median and tail radial errors were larger, making the precision-efficiency trade-off more pronounced.
A separate acceptance estimate illustrates why the reconstructed radius matters for background studies. In the simulated samples, 1.02% of Compton electrons projected back to the target foil within 4.5 cm of the true vertex, compared with 0.0091% within 4.3 mm, the best 50% containment radius reported. The authors state that this corresponds to a factor-of-110 background reduction relative to the cited ILL comparison, but it is a simulation-based estimate under the chosen stress-test conditions, not a measured background rate.
A result still waiting for detector data
The findings are limited to synthetic HIBEAM detector simulations and the five injected-background settings. The detector response was simplified to sampled hit positions and independent coordinate smearing. The Compton stress test used a fixed 5 MeV energy and isotropically generated inward directions.
The comparison is therefore a set of point estimates from simulated stress-test samples, and the supplied analysis reports no confidence intervals. It also fixes the reconstructed z coordinate to the foil plane. The document is an arXiv preprint, version 1, dated 28 August 2026.
For now, the comparison points to a design choice rather than a definitive champion. The authors conclude that classical and machine-learning methods are comparable for vertex coordinates in these simulated events, while machine-learning methods provide additional event-shape information.
The majority of the work was funded by the Olle Engkvist Foundation, with additional support from the Swedish Research Council, STINT, FAPERJ, CAPES and CNPq. Computational resources were provided by NAISS through LUNARC.
Paper data and sources
Original title: Vertex reconstruction for a search for neutron-antineutron conversions with HIBEAM
Authors: Alexander Burgman, Sze Chun Yiu, Yamna Shaikh et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text