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A neural network clustering algorithm for the ATLAS silicon pixel detector

ATLAS collaboration

arXiv:1406.7690v1hep-ex

TL;DR

Merged pixel clusters in dense environments can create shared track measurements that degrade track quality. The paper applies neural networks to identify and split those clusters, reporting fewer shared measurements and improved position and impact-parameter resolution.

  • Problem

    Merged clusters in dense particle environments can create shared measurements that degrade track quality, while correctly modeling shared measurements matters for track-efficiency systematic uncertainties.

    Source: §1 · p. 4

  • Method

    A set of neural networks identifies and splits merged clusters in the ATLAS pixel detector, with additional networks estimating cluster positions and uncertainties.

    Source: §1 · p. 4, §5 · p. 18

  • Results

    Approximately a factor of three reduction in measurements assigned to multiple tracks is reported, alongside significantly improved impact-parameter resolution even for isolated tracks.

    Source: §1 · p. 4, §5 · p. 18

  • Takeaways & Limitations

    The neural-network clustering became the default ATLAS approach for the remainder of 2011 data-taking, and performance agreed well between simulation and proton–proton collision data.

    Source: §1 · p. 5, §5 · p. 19

    Time-dependent radiation effects are not included in the simulation and may need consideration after significant detector radiation damage.

    Source: §3.2 · p. 13

Abstract

from arXiv · show

A novel technique to identify and split clusters created by multiple charged particles in the ATLAS pixel detector using a set of artificial neural networks is presented. Such merged clusters are a common feature of tracks originating from highly energetic objects, such as jets. Neural networks are trained using Monte Carlo samples produced with a detailed detector simulation. This technique replaces the former clustering approach based on a connected component analysis and charge interpolation. The performance of the neural network splitting technique is quantified using data from proton--proton collisions at the LHC collected by the ATLAS detector in 2011 and from Monte Carlo simulations. This technique reduces the number of clusters shared between tracks in highly energetic jets by up to a factor of three. It also provides more precise position and error estimates of the clusters in both the transverse and longitudinal impact parameter resolution.

1. Introduction

Track reconstruction in ATLAS relies on pixel-detector measurements, but merged clusters in dense particle environments can leave measurements shared between tracks and degrade their position estimates. The paper introduces neural-network clustering to split these clusters, reducing shared measurements by approximately a factor of three.

1. Introduction

  • The inner detector combines pixel, microstrip, and straw-tube tracking technologies to reconstruct charged-particle trajectories within |η| < 2.5.The pixel detector is at the innermost radii, inside the silicon microstrip detector and transition radiation tracker.Source: §1 · p. 3
  • The inside-out track-finding sequence forms seeds from nearby-layer clusters, adds measurements along a road, and then uses ambiguity processing to rank candidates and suppress fakes and duplicates.Measurements assigned to multiple candidates are termed shared; holes are expected active modules without an assigned measurement.Source: §1 · p. 4
  • In collimated environments such as energetic-jet cores, merged clusters can produce shared measurements that degrade reconstructed track quality.Shared measurements are nevertheless allowed in small numbers to avoid compromising track-reconstruction efficiency.Source: §1 · p. 4
  • Approximately a factor of three reduction in measurements assigned to multiple tracks is reported for the neural-network cluster-splitting technique.The introduction also reports improved precision of cluster position estimates and track performance.Source: §1 · p. 4
  • The neural-network clustering became ATLAS’s default approach for the remainder of 2011 data-taking, and earlier 2011 data were reprocessed for consistency.The studies used only a small fraction of the 2011 dataset because statistical uncertainty was negligible.Source: §1 · p. 5

2. Cluster measurements with the ATLAS pixel detector

The pixel detector measures charged-particle trajectories through clusters of pixel hits, whose positions are refined using collected charge. In dense environments, the former connected-component approach can merge deposits from nearby particles, limiting their separate reconstruction.

2. Cluster measurements with the ATLAS pixel detector

  • The pixel system supports impact-parameter measurements, with transverse d0 and longitudinal z0 components; the stated approximate resolution parameterization is averaged over η.The quoted design resolutions are σd0 = 140 [µm GeV]/pT[GeV] ⊕ 10 µm and σz0 sinθ = 209 [µm GeV]/pT[GeV] ⊕ 91 µm.Source: §2 · pp. 5–6
  • The pixel system has three barrel layers and three discs on each side, with typical pixel sizes of 50 µm transversely and 400 µm longitudinally.The longitudinal size is 600 µm in regions between readout chips.Source: §2 · p. 5, Figure 1 · p. 6
  • For primary charged particles with pT > 400 MeV, cluster sizes range from 1.4 to 3 pixels transversely and 1 to approximately 3.5 pixels longitudinally.A δ-ray can enlarge a cluster or change its charge and bias its estimated position.Source: §2 · p. 6
  • A charged particle typically deposits charge across multiple pixels, and CCA groups neighbouring pixels using eight-cell connectivity to form clusters.Charge interpolation uses measurements from the first and last rows and columns to refine the estimated intersection position.Source: §2 · pp. 5–7
  • When particles approach within pixel granularity, CCA can merge their deposits into shared clusters, and tracks may be discarded if shared measurements exceed a threshold.The resulting inefficiency can affect both tracks in a close pair.Source: §2 · pp. 7–8

3. Pixel cluster splitting

The section presents neural-network clustering to identify and split merged pixel clusters, estimate particle impact positions and uncertainties, and adapt track reconstruction to the improved cluster information.

3. Pixel cluster splitting

  • The algorithm can flag merged clusters for dedicated calibration or ambiguity resolution, and split them into per-particle measurements when possible.Splitting can improve double-track resolution and reduce shared measurements.Source: §3 · p. 9

3.1 A neural network for cluster splitting

  • The NN processes only clusters fitting a 7×7-pixel matrix; excluded large clusters are under 1% and do not affect high-pT tracking.The excluded clusters most probably arise from particles not originating from beam collisions; the paper attributes the lack of high-pT impact to their pT<0.4 GeV tracks being below the reconstruction threshold.Source: §3.1 · p. 10
  • In the first pass, particles are assumed to originate at the beam-interaction center; after track candidates are identified, the algorithm reruns using refined incident-angle estimates.No further splitting is attempted in that later pass because initial pattern recognition is run only once.Source: §3.1 · p. 10
  • A classifier estimates whether clusters contain one to three particles; clusters are split above Pshared > 0.5 and labeled merged above 0.02.The algorithm assumes at most three particles per cluster.Source: §3.1 · pp. 9, 11
  • Three interpolation networks estimate 2D impact positions by particle count; six further networks estimate residual PDFs, whose second moments supply track-fit uncertainties.The position networks use training samples selected by the true particle count.Source: §3.1 · pp. 11–12

3.2 Neural network training

  • Ten networks are trained on mixed simulated top–antitop and high-energy dijet samples passed through GEANT4; time-dependent radiation effects are omitted.The training procedure uses independent testing samples to determine when the mean-square error reaches a minimum.Source: §3.2 · pp. 12–13

3.3 Changes to the track reconstruction

  • Track finding uses a combinatorial filter to consider multiple nearby measurements, including split clusters within low-momentum extrapolation uncertainty.Ambiguity processing can reject fake candidates more efficiently because shared measurements are reduced; sharing remains possible for unsplit clusters compatible with merging.Source: §3.3 · p. 13

4. Performance of the neural network clustering algorithm

The neural-network algorithm splits merged pixel clusters and improves their position estimates. It reduces shared measurements in the core of high-energy jets, while data comparisons also show improved residual and impact-parameter resolution.

4. Performance of the neural network clustering algorithm

  • At the chosen working point, 71% of two-particle clusters are correctly split, while 7.5% of one-particle clusters are incorrectly split.The working point is for the setup without track information.Source: §4 · p. 14, Figure 6 · p. 15
  • Track-angle information improves the incorrectly split-cluster rate by approximately a factor of two at 71% efficiency, but is used only to improve resolution and error estimates.The current track-reconstruction strategy has no additional track-finding pass after fitting, so track-informed splitting cannot resolve shared clusters or recover lost tracks.Source: §4 · p. 14
  • For three- and four-pixel-wide transverse clusters, NN clustering improves residuals and removes the double-peak structure seen with CCA.Non-Gaussian NN residual tails are attributed to large-angle scattering, δ-rays not included in training labels, and skewed distributions at module edges.Source: §4 · pp. 14–15, Figure 7 · p. 16

4.1 Performance in data and simulation

  • Performance and data-simulation agreement depend on modeling silicon interactions and signal collection; barrel and endcap clusters are treated similarly with detector region supplied to the network.Cluster merging depends on local charged-particle density, Lorentz drift, and incident angles; charge collection and channel cross-talk are considered negligible.Source: §4.1 · pp. 15–16
  • Relative NN-versus-CCA residual-resolution improvements are largely consistent between data and simulation, despite longitudinal discrepancies likely linked to charge-sharing modeling.Transverse gains are mostly attributed to splitting, while nonlinear charge interpolation contributes substantially to longitudinal gains.Source: §4.1 · p. 16, Figure 8 · p. 17
  • For selected isolated muons, NN clustering improves z0 resolution by 7% and d0 resolution by 3% compared with CCA.At central η, z0 resolution does not improve because normal-incidence clusters are one pixel wide longitudinally, preventing interpolation.Source: §4.1 · pp. 16–17, Figure 9 · p. 17
  • A factor of three fewer shared measurements in the jet core is obtained with NN clustering, and simulation accurately describes the rate and reduction.The comparison uses tracks in jets with 500 < pT < 600 GeV.Source: §4.1 · pp. 17–18, Figure 10 · p. 18
  • The NN algorithm runs approximately six times slower than CCA, but adds at most 5% to per-event execution time under the highest 2012 pile-up conditions.The event-time estimate includes splitting, reevaluation during track fitting, and additional track-candidate combinations.Source: §4.1 · p. 18

5. Conclusion

The neural-network method reduces measurements assigned to multiple tracks, particularly in highly energetic jet cores. Additional networks improve cluster-position estimates, and performance agrees between simulation and proton–proton collision data.

  • A factor of three reduction in measurements assigned to multiple tracks is achieved, particularly in the cores of highly energetic jets.Source: §5 · p. 18
  • An additional set of neural networks estimates cluster positions and uncertainties, significantly improving impact parameter resolution even for isolated tracks.Source: §5 · p. 18
  • Neural-network performance agrees between Monte Carlo simulation and experimental proton–proton collision data.Source: §5 · p. 19
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