Internal alignment of the SLD vertex detector using a matrix singular value decomposition technique

The tracking resolution and vertex finding capabilities of the SLD experiment depend upon a precise knowledge of the location and orientation of the 96 elements of the SLD pixel vertex detector (VXD3) in 3D space. At the heart of the deterministic procedure described here to align the 96 CCDs is the matrix inversion technique of singular value decomposition (SVD). This tool is employed to unfold the detector geometry corrections from the track hit residual data in the VXD3. The algorithm is adapted to perform an optimal χ2 minimization by careful treatment of the errors and correlations in the residual measurements. The general form of the problems that might be solved with this technique is discussed. The tracking resolution obtained with the aligned geometry is compared with the starting point, based on an optical survey of the CCDs, and is shown to achieve the design performance.