Graph Neural Network-Based Pipeline for Track Finding in the Velo at LHCb

TL;DR

The paper tackles real-time track reconstruction in the LHCb Velo under high data rates by proposing ETX4VELO, a Graph Neural Network–based pipeline inspired by Exa.TrkX and designed for the GPU-driven Allen trigger. It introduces a five-stage pipeline that adds a triplet-based disambiguation step to handle tracks sharing hits, achieving near-linear throughput scaling with the number of hits and competitive physics performance. Across evaluations, ETX4VELO reduces fake tracks from about $2\%$ to well below $1\%$ and improves electron reconstruction compared to the legacy Allen algorithm, particularly for Velo-only electrons. The work demonstrates the viability of deploying GNN-based track finding in real-time, outlines integration plans with Allen, and provides a path for extending to other detectors like SciFi.

Abstract

Over the next decade, increases in instantaneous luminosity and detector granularity will amplify the amount of data that has to be analysed by high-energy physics experiments, whether in real time or offline, by an order of magnitude. The reconstruction of charged particle tracks, which has always been a crucial element of offline data processing pipelines, must increasingly be deployed from the very first stages of the real time processing to enable experiments to achieve their physics goals. Graph Neural Networks (GNNs) have received a great deal of attention in the community because their computational complexity scales nearly linearly with the number of hits in the detector, unlike conventional algorithms which often scale quadratically or worse. This paper presents ETX4VELO, a GNN-based track-finding pipeline tailored for the Run 3 LHCb experiment's Vertex Locator, in the context of LHCb's fully GPU-based first-level trigger system, Allen. Currently implemented in Python, ETX4VELO offers the ability to reconstruct tracks with shared hits using a novel triplet-based method. When benchmarked against the traditional track-finding algorithm in Allen, this GNN-based approach not only matches but occasionally surpasses its physics performance. In particular, the fraction of fake tracks is reduced from over 2% to below 1% and the efficiency to reconstruct electrons is improved. While achieving comparable physics performance is a milestone, the immediate priority remains implementing ETX4VELO in Allen in order to determine and optimise its throughput, to meet the demands of this high-rate environment.

Figures (7)

• Figure 1: Sketch of the LHCb tracking system in Run 3.
• Figure 2: Simplified example of tracks to be reconstructed in the Velo. The blue and purple tracks share three hits prior to diverging. The purple track jumps from plane 3 to 5, missing 4. The orange track intersects the blue and purple tracks. Dark points represent hits unassociated with any particle. When considering the hits as graph nodes, lines between hit nodes represent the genuine edges, as defined in this work.
• Figure 3: Illustration of the pipeline's 5 stages, beginning with hits from the minimalist example in Figure \ref{['fig:tracks']}. Steps entail (1) building a rough hit graph, (2) classifying its edges and discarding fakes (in red), (3) constructing the edge graph with edge-to-edge connections called triplets, (4) classifying and removing fake triplets, and finally, producing the tracks.
• Figure 4: Schematic of the GNN architecture, highlighting: (1) hit and edge encodings, (2) iterative message passing refinement, and (3) subsequent edge and triplet classifications. The node and edge encoders and networks and the edge and triplet classifiers are DNNs.
• Figure 5: Visual representation of the three triplet configurations in the edge graph: (a) the articulation, (b) the left elbow and (c) the right elbow.