Reconstruction of overlapping electromagnetic showers in calorimeters using Transformers

Abstract Accurate clustering of electromagnetic energy deposits is essential for reconstructing photons and electrons in modern hadron collider experiments, where boosted topologies and pileup often cause overlapping showers and ambiguous energy assignment. We present deep learning-based clustering approaches that reconstruct particle energy and impact position directly from calorimeter readout. The study includes a two-step strategy in which candidate seed windows are identified and then jointly processed via distance-weighted message passing or attention mechanism, and a single-step graph transformer, ClusTEX, which performs candidate selection and reconstruction in one inference stage. ClusTEX uses a novel positional encoding scheme that separates local coordinates within the graph from global detector coordinates, enabling efficient, geometry-aware inference. Models are trained on Geant4 simulations of a simplified toy calorimeter and an ECAL-inspired topology with an explicit $$(\eta , \phi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>η</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> dependence. Performance is evaluated using efficiency, energy and position resolutions, background rejection, and “splitting rate” – the probability to reconstruct two objects for a single-photon shower. In the toy calorimeter, attention-based interactions improve the reconstruction of overlapping showers relative to both the standard algorithm and distance-driven message passing, while maintaining performance on isolated photons and reducing splitting without multi-pass inference. In boosted $$\pi ^0 \rightarrow \gamma \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> events, the attention-based model retains di-photon mass reconstruction capability, where the standard algorithm becomes inefficient. In the ECAL-inspired topology, ClusTEX provides the best overall performance, yielding improved energy resolution and reduced splitting compared to two-step approaches and the standard algorithm. ClusTEX also remains robust under localized detector failures, showing improved stability and partial recovery of energy in non-responsive channels.