Fig. 2: Main results of the vertex-activity (VA) fitting algorithm on the testing dataset, consisting of events with one muon and one to five protons.

μ: mean, σ: standard deviation, false positives (negatives): over (under)-reconstructed particles (with default true (reconstructed) values: kinetic energy (KE) = 0 MeV; θ = 90 degrees; ϕ = 180 degrees). a Histogram of the total vs reconstructed KE for each event, including false positives and false negatives; KE resolution per particle relative to true KE and momentum (P) for each fitted particle, excluding false positives and false negatives; distribution of the difference between the reconstructed KE and the true KE per particle for the cases with 1–5 particles per event, including false positives and false negatives. b Confusion matrix showing the recall (normalisation by columns) and precision (normalisation by rows) of the true vs reconstructed number of particles; distribution of the false positives (particles predicted by the algorithm that are not present in the input events) and false negatives (particles not predicted by the algorithm that are present in the input events). c Density plot relating the difference between reconstructed and true ϕ and θ (spherical coordinates) per particle; density plot relating the difference between reconstructed and true angles and the particle length. Both plots include false positives and false negatives. d. Scatter plot comparing the true and reconstructed vertex per event for the x, y, and z coordinates; box plot of the 3D Euclidean distance between the reconstructed and true vertices for the cases with 1–5 particles per event.