Alignment of the CMS tracker with LHC and cosmic ray data

TL;DR

This work documents a comprehensive, track-based alignment procedure for the CMS silicon tracker, employing Millepede II with General Broken Lines track modelling to fit hundreds of thousands of alignment parameters while accounting for multiple scattering. It integrates sensor-level shape parameters, hierarchical constraints, and time-differential alignment, validated through cosmic-ray and proton-proton data, Z→μμ decays, and calorimeter cross-checks, achieving sub-10 μm precision and robust control of weak modes. The strategy combines large-scale structure monitoring (LAS and vertex residuals) with resonance constraints to ensure stable, high-quality track reconstruction across 2011 data-taking, enabling the CMS tracker to exploit its intrinsic silicon-resolution capabilities. The results demonstrate a fast, parallelized workflow capable of handling CMS’s unprecedented tracker complexity and delivering reliable geometry updates for prompt reconstruction and physics analyses.

Abstract

The central component of the CMS detector is the largest silicon tracker ever built. The precise alignment of this complex device is a formidable challenge, and only achievable with a significant extension of the technologies routinely used for tracking detectors in the past. This article describes the full-scale alignment procedure as it is used during LHC operations. Among the specific features of the method are the simultaneous determination of up to 200,000 alignment parameters with tracks, the measurement of individual sensor curvature parameters, the control of systematic misalignment effects, and the implementation of the whole procedure in a multi-processor environment for high execution speed. Overall, the achieved statistical accuracy on the module alignment is found to be significantly better than 10 micrometers.

Figures (19)

• Figure 1: Schematic view of one quarter of the silicon tracker in the $r$-$z$ plane. The positions of the pixel modules are indicated within the hatched area. At larger radii within the lightly shaded areas, solid rectangles represent single strip modules, while hollow rectangles indicate pairs of strip modules mounted back-to-back with a relative stereo angle. The figure also illustrates the paths of the laser rays (R), the alignment tubes (A) and the beam splitters (B) of the laser alignment system.
• Figure 2: Sketch of a silicon strip module showing the axes of its local coordinate system, $u$, $v$, and $w$, and the respective local rotations $\alpha$, $\beta$, $\gamma$ (left), together with illustrations of the local track angles $\psi$ and $\zeta$ (right).
• Figure 3: Dependence of the total $\chi^2$ of the track fits, divided by the number of tracks, on the assumed $\theta_x$ (left) and $\theta_y$ (right) tilt angles for $\lvert \eta \rvert<2.5$ and $p_{\mathrm{T}}$$>1$${\,\text{Ge\spaceV\space/\space}c}$. The error bars are purely statistical and correlated point-to-point because the same tracks are used for each point.
• Figure 4: Tracker tilt angles $\theta_x$ (filled circles) and $\theta_y$ (hollow triangles) as a function of track pseudorapidity. The left plot shows the values measured with the data collected in 2010; the right plot has been obtained from simulated events without tracker misalignment. The statistical uncertainty is typically smaller than the symbol size and mostly invisible. The outer error bars indicate the RMS of the variations which are observed when varying several parameters of the tilt angle determination. The shaded bands indicate the margins of $\pm$0.1 discussed in the text.
• Figure 5: The three two-dimensional second-order polynomials to describe sensor deviations from the flat plane, illustrated for sagittae $w_{20} = w_{11} = w_{02} = 1$.