Alignment of the CMS Silicon Tracker during Commissioning with Cosmic Rays

TL;DR

This work presents the first full alignment of the CMS silicon tracker using over three million cosmic-ray tracks at 3.8 T, augmented by optical surveys and the Laser Alignment System. It achieves module-position precisions of about 3–4 μm in the barrel and 3–14 μm in the endcaps, with track-parameter resolutions close to the design target. Two complementary track-based alignment algorithms, Millepede II (global) and Hits and Impact Points (HIP, local), are used and combined to exploit global correlations and track-level consistency, validated against detailed MC simulations and LAS measurements. The results establish a robust, multi-input alignment framework ready for LHC collision data and provide critical groundwork for achieving CMS physics goals.

Abstract

The CMS silicon tracker, consisting of 1440 silicon pixel and 15148 silicon strip detector modules, has been aligned using more than three million cosmic ray charged particles, with additional information from optical surveys. The positions of the modules were determined with respect to cosmic ray trajectories to a precision of 3-4 microns RMS in the barrel and 3-14 microns RMS in the endcap in the most sensitive coordinate. The results have been validated by several methods, including the laser alignment system, and compared with predictions obtained from simulation. Correlated systematic effects have been investigated. The track parameter resolutions obtained with this alignment are close to the design performance.

Figures (15)

• Figure 1: A quarter of the CMS silicon tracker in an $rz$ view. Single-sided silicon strip module positions are indicated as solid light (purple) lines, double-sided strip modules as open (blue) lines, and pixel modules as solid dark (blue) lines. Also shown are the paths of the laser rays (R), the beam splitters (B), and the alignment tubes (A) of the Laser Alignment System.
• Figure 2: Illustration of the module local coordinates $u,v,w$ and the corresponding rotations $\alpha,\beta,\gamma$ for a single-sided strip module.
• Figure 3: Momentum (left), azimuthal angle (middle), and polar angle (right) spectra of cosmic muons reconstructed in the CMS tracker volume based on the selection criteria described in the text. The solid (red) circles represent the cosmic ray data whereas the open (blue) circles come from a MC simulation. The vertical cosmic ray tracks correspond approximately to $\phi=\theta=90^\circ$.
• Figure 4: Distributions of normalized track residuals after the APE calibration procedure: BPIX (left), TIB (center), and TOB (right). Solid lines represent the results of Gaussian fits and the fit mean and sigma values are given within the plots. The alignment obtained from the combined method was used.
• Figure 5: Distributions of the $\chi^2/\mathrm{ndf}$ of the tracks before alignment (dotted line) and after alignment with the local (dashed-dotted line), global (dashed line), and combined (solid line) methods.