Clustering of Electromagnetic Showers and Particle Interactions with Graph Neural Networks in Liquid Argon Time Projection Chambers Data

Liquid Argon Time Projection Chambers (LArTPCs) are a class of detectors that produce high resolution images of charged particles within their sensitive volume. In these images, the clustering of distinct particles into superstructures is of central importance to the current and future neutrino physics program. Electromagnetic (EM) activity typically exhibits spatially detached fragments of varying morphology and orientation that are challenging to efficiently assemble using traditional algorithms. Similarly, particles that are spatially removed from each other in the detector may originate from a common interaction. Graph Neural Networks (GNNs) were developed in recent years to find correlations between objects embedded in an arbitrary space. GNNs are first studied with the goal of predicting the adjacency matrix of EM shower fragments and to identify the origin of showers, i.e. primary fragments. On the PILArNet public LArTPC simulation dataset, the algorithm developed in this paper achieves a shower clustering accuracy characterized by a mean adjusted Rand index (ARI) of 97.8 % and a primary identification accuracy of 99.8 %. It yields a relative shower energy resolution of $(4.1+1.4/\sqrt{E (\text{GeV})})\,\%$ and a shower direction resolution of $(2.1/\sqrt{E(\text{GeV})})^{\circ}$. The optimized GNN is then applied to the related task of clustering particle instances into interactions and yields a mean ARI of 99.2 % for an interaction density of $\sim\mathcal{O}(1)\,m^{-3}$.