Description and performance of track and primary-vertex reconstruction with the CMS tracker (1405.6569v2)

Abstract: A description is provided of the software algorithms developed for the CMS tracker both for reconstructing charged-particle trajectories in proton-proton interactions and for using the resulting tracks to estimate the positions of the LHC luminous region and individual primary-interaction vertices. Despite the very hostile environment at the LHC, the performance obtained with these algorithms is found to be excellent. For ttbar events under typical 2011 pileup conditions, the average track-reconstruction efficiency for promptly-produced charged particles with transverse momenta of pt > 0.9 GeV is 94% for pseudorapidities of abs(eta) < 0.9 and 85% for 0.9 < abs(eta) < 2.5. The inefficiency is caused mainly by hadrons that undergo nuclear interactions in the tracker material. For isolated muons, the corresponding efficiencies are essentially 100%. For isolated muons of pt = 100 GeV emitted at abs(eta) < 1.4, the resolutions are approximately 2.8% in pt, and respectively, 10 microns and 30 microns in the transverse and longitudinal impact parameters. The position resolution achieved for reconstructed primary vertices that correspond to interesting pp collisions is 10-12 microns in each of the three spatial dimensions. The tracking and vertexing software is fast and flexible, and easily adaptable to other functions, such as fast tracking for the trigger, or dedicated tracking for electrons that takes into account bremsstrahlung.

• The paper demonstrates that the CMS tracker employs advanced iterative algorithms, including the Combinatorial Track Finder, to effectively handle high-luminosity collisions.
• Track reconstruction utilizes a six-step iterative approach, achieving up to 94% efficiency in the barrel region and precise impact parameter resolutions around 10 microns.
• Primary-vertex reconstruction uses deterministic annealing with adaptive vertex fits to reliably identify vertices even amid significant pileup.

An Overview of Track and Primary-Vertex Reconstruction Performance with the CMS Tracker

The CMS paper describes the development and performance of software algorithms for track and primary-vertex reconstruction in the CMS tracker, situated at the Large Hadron Collider (LHC). These algorithms are crafted to operate in the challenging environment characterized by high-luminosity proton-proton (pp) collisions of the LHC, demanding efficient reconstruction amidst substantial pileup events. This summary articulates the core methodologies and results presented in this comprehensive paper.

Algorithmic Approach

The track reconstruction relies on the Combinatorial Track Finder (CTF), which is an extension of the Kalman filter tailored for conditions in high particle occupancy environments. The reconstruction process utilizes six iterative steps, each designed to optimize for different track characteristics and utilize varying constraints and configurations. Initial iterations focus on high transverse momentum (\pt) tracks, relying heavily on pixel data, while subsequent iterations address lower \pt and displaced tracks. This iterative approach helps manage the computational complexity and enhances reconstruction accuracy.

The primary-vertex reconstruction employs deterministic annealing for clustering track data into distinct collision vertices, followed by an adaptive vertex fit to ascertain vertex positions accurately. This methodology addresses track-to-vertex assignment challenges, particularly in high pileup scenarios, ensuring a robust minimization of the reconstructive error.

Performance Metrics

For high-energy muons, reconstruction efficiency is reported as nearly perfect across the tracked pseudorapidity range, emphasizing the resistance of muon trajectories to interactions with the detector material. In contrast, for charged hadrons, the efficiency is slightly reduced owing to nuclear interactions within the tracker. For transverse momenta \pt greater than 0.9 GeV, the overall efficiency for promptly produced particles in \ttbar events achieves 94% in the barrel and 85% in the forward regions, displaying slight reductions due to material interactions and geometrical coverage gaps.

The algorithms maintain low fake rates, typically below a few percent, indicating high fidelity in track reconstruction even under high pileup conditions. The resolutions achieved for track parameters underscore the precision of the CMS tracker, with impact parameter resolutions reaching the order of 10 microns for high-\pt tracks.

Software Efficiency

The computational efficiency of these algorithms is paramount given the high data rates from LHC operations. The software exhibits significant adaptability, demonstrated by its use in the CMS high-level trigger (HLT), facilitating real-time data filtering and processing requirements. Within the HLT context, algorithms are modified to ensure rapid execution, balancing accuracy with computational load.

Practical and Theoretical Implications

Practically, the impressive resolution and efficiency metrics of the CMS tracking system enhance the accuracy of CMS physics analyses, from precision cross-section measurements to rare decay searches. Theoretically, these advancements push the boundaries of achievable precision in high-energy physics experiments, suggesting further work could investigate real-time adaptive algorithms to better handle future LHC conditions, especially with increasingly higher collision rates expected.

The methods presented and demonstrated by the CMS tracker algorithm suite reaffirm the critical importance of advanced tracking software in contemporary high-energy physics, laying a groundwork for future enhancements and adaptations in tracking paradigms at large-scale experimental setups.