End-to-end event reconstruction for precision physics at future colliders

Abstract

Future collider experiments require unprecedented precision in measurements of Higgs, electroweak, and flavour observables, placing stringent demands on event reconstruction. The achievable precision on Higgs couplings scales directly with the resolution on visible final state particles and their invariant masses. Current particle flow algorithms rely on detector specific clustering, limiting flexibility during detector design. Here we present an end-to-end global event reconstruction approach that maps charged particle tracks and calorimeter and muon hits directly to particle level objects. The method combines geometric algebra transformer networks with object condensation based clustering, followed by dedicated networks for particle identification and energy regression. Our approach is benchmarked on fully simulated electron positron collisions at FCC-ee using the CLD detector concept. It outperforms the state-of-the-art rule-based algorithm by 10--20\% in relative reconstruction efficiency, achieves up to two orders of magnitude reduction in fake-particle rates for charged hadrons, and improves visible energy and invariant mass resolution by 22\%. By decoupling reconstruction performance from detector-specific tuning, this framework enables rapid iteration during the detector design phase of future collider experiments.

Figures (11)

• Figure 1: Overview of the HitPf reconstruction pipeline compared to conventional Particle Flow algorithms. Traditional approaches rely on sequential, hand-tuned stages that first cluster calorimeter hits before associating them with tracks and assigning particle properties. HitPf bypasses these intermediate steps, reconstructing final state particles directly from detector hits in a single end-to-end trainable model.
• Figure 2: Architecture of the candidate determination step. The network takes as input detector hits from all sub-detectors and outputs particle candidate clusters. Left (blue): the encoder maps hit features into multivectors in a geometric algebra representation. Centre (grey): a Geometric Transformer performs $M$ GATr message-passing rounds over latent graphs $G_0, \ldots, G_M$; shaded blocks indicate trainable components. Right (green): the decoder extracts point and scalar components from the output multivectors and performs density-peak clustering (DPC). Each hit is assigned a local density $\rho$ and a distance $\delta$ to the nearest node of higher density; cluster centres are identified as nodes with simultaneously high $\rho$ and high $\delta$.
• Figure 3: Section of a $Z\rightarrow q\bar{q}$ event showing the target hit assignment (left), the HitPf reconstruction (center), and the PandoraPfa reconstruction (right). The event showcases two overlapping showers originating from a $K_L$ and a photon. The colour assigned to each hit for HitPf and PandoraPfa corresponds to the MC particle contributing the largest hit count to the reconstructed cluster. The bottom subplot in each panel shows the two showers projected along the shower axis.
• Figure 4: Particle identification performance as a function of energy for charged hadrons (left), photons (centre), and neutral hadrons (right). Top row: reconstruction efficiency, defined as the fraction of target particles reconstructed with the correct label, shown as a function of the matched MC particle energy. Bottom row: fake rate, defined as the fraction of reconstructed candidates without a matched target particle, shown as a function of the energy of the reconstructed particle.
• Figure 5: Confusion matrices comparing HitPf (top entry of each tile (%)) and PandoraPfa (bottom entry of each tile (%)) across two energy ranges: 1--10 GeV (left), and 10--100 GeV (right). Rows correspond to true particle type and columns to reconstructed type. Diagonal entries indicate correct identification, off-diagonal entries show mis-identification rates. The "missed" column represents the fraction of particles not reconstructed. The "fake" row indicates the percentage of reconstructed candidates in each class without a matched target particle. All values are normalized per row, except for the fake rates, which are normalized by column.