Alignment of the CMS Preshower detector

Abstract The Preshower detector, as part of the CMS endcap electromagnetic calorimeter, is designed to identify π 0 in the endcaps within a fiducial region 1.653 | η | 2.6 . It is based on 4288 silicon sensors, each with active area 61 × 61 mm 2 segmented into 32 strips with 1.9  mm pitch. For minimum ionizing particles the intrinsic spatial precision is 17.6 mm parallel to the strip and 550 μ m perpendicular to the strips. Exploiting its spatial resolution relies upon excellent alignment with the neighboring detectors, especially the Tracker. The alignment is based on the extrapolation of tracks from the Tracker to the Preshower and gives an alignment precision of a few millimeters for translation and a few milliradians for rotation. The method for Preshower alignment is discussed and the results of the alignment with respect to the Tracker, using LHC collision data collected by CMS in 2011, are given.


Introduction
The Preshower (ES) is designed to identify π 0 in the endcaps within a fiducial region 1.653 < |η| < 2.6. It also improves the Endcap ECAL (EE) position determination of electrons and photons with its fine granularity. ES is formed from two orthogonal planes in each endcap, mounted with 4288 silicon sensors in total [1]. The planes are known as ES+F, ES+R, ES-F, and ES-R reflecting the nomenclature of the endcaps (+ or -) and whether the plane is Front (closest to the interaction point) or Rear [2]. In front of each plane of sensors is a sheet of lead, to initiate electromagnetic showers: 2X 0 in the front plane and 1X 0 in the rear plane. The active area of each sensor is 61 × 61 mm 2 , segmented into 32 strips [1]. Figure 1: Photo of the Preshower "micromodule" containing the 61 × 61 mm 2 silicon sensor (32 strips at 1.9 mm pitch) bonded to the front-end electronics.

Preprint submitted to Elsevier
February 24, 2012 For minimum ionizing particles the intrinsic spatial precision is 1.76 cm parallel to the strips and 550 µm perpendicular to the strips.
For optimum performance the ES needs to be aligned with respect to the Tracker within the expected spatial precision. The alignment framework uses LHC collision data taken with CMS in 2011.

Algorithm
The ES alignment relies on the minimization of the residuals of the differences between the positions of charged tracks measured in the ES and those predicted by the Tracker.
The alignment procedure begins by selecting high quality tracks reconstructed in the Tracker: at least 10 hits (including 1 in the outermost Tracker layer) and p T > 1.5 GeV/c. The selection was refined by taking only tracks pointing to a restricted fiducial region in the endcaps, 1.7 < |η| < 2.3 and not pointing to dead ES areas [2].
The track trajectories are propagated to the ES (roughly 3m from the collision point) using the Stepping Helix propagator [3], which provides extrapolation by using finite helix length with the magnetic field and material effects at each step. The extrapolation error is less than 1 cm. A search window with radius 30 mm is then opened, for matching the measured ES hits and the predicted point. With the residual vector pointing from a measured hit to a predicted point in the local coordinate on the ES plane, the χ 2 is defined below.
where i is the residual vector pointing from the measured ES hit to the predicted point, in the local coordinate system for track i, and V is the covariance matrix from the extrapolation uncertainty and the ES spatial precision. N is the number of selected tracks.
For calculating the 3 translational and 3 rotational alignment parameters, a least-squares method is used and a minimization is performed by adjusting the alignment vector P (6×1) iteratively, where P [4], where J i is a Jacobian matrix, and J i,6×2 is reduced to a function of position and momentum at the predicted point. The angular terms of J i,6×2 are reduced with the assumption of straight line trajectories over small rotational angles. The local origin of ES is moved iteratively from the ideal position in the global coordinate system by using the vector P . Then, P becomes stable at the order of millimeters or milliradians as χ 2 /N approaches its minimum. Figure 3 shows the translational residuals between the ES hit positions and the Tracker predictions, before and after the alignment has been performed, for all four planes. They show that there is a relative vertical mis-alignment between the Tracker and ES endcaps of about 9 mm (shown by the ES+R plane) and 7 mm (ES-R). There is also a horizontal mis-alignment, but only between the ES+ and the Tracker, of about 5 mm. After software alignment the ES is aligned (translationally) to the Tracker to better than 0.15 mm, well within the intrinsic spatial precision of the ES. Figure 4 represents the amount of rotational mis-alignment for the two planes of ES+, corresponding to rotations with respect to the nominal of 1 or 2 milliradians. With the aligned ES geometry, we have measured the precision of the ES position measurement with high energy tracks (p T > 20 GeV/c), where the extrapolation error from the Tracker and the effects of multiple scattering are minimized. The calculated ES precision σ preshower is given by:

Results
where σ total are the fitted Gaussian widths from the residual plots in Figure 5 and σ track is the average trajectory prediction error from the Tracker to ES. The expected precision for minimum ionizing particles is about 1.9 mm/ √ 12 = 550 µm. For the four ES planes the average tracker error is 500 µm, and the total width is 800 µm, which is the fitted Gaussian width weighted by the number of selected tracks in the ES planes, leading to a measured preshower precision of around 600 µm, in good agreement with prediction. 3

Summary
A systematic procedure for aligning the Preshower with respect to the Tracker has been developed and applied. After alignment, the spatial precision for minimum ionizing particles in the Preshower is as expected, around 600 µm.