Alignment of the CMS silicon tracker using Millepede II

The positions of the silicon modules of the CMS tracker will be known to $O(100$ $\mu$m) from survey measurements, mounting precision and the hardware alignment system. However, in order to fully exploit the capabilities of the tracker, these positions need to be known to a precision of a few $\mu$m. Only a track-based alignment procedure can reach this required precision. Such an alignment procedure is a major challenge given that about 50.000 geometry constants need to be measured. Making use of the novel $\chi^2$ minimization program Millepede II an alignment strategy has been developed in which all detector components are aligned simultaneously and all correlations between their position parameters taken into account. Tracks from different sources such as Z$^0$ decays and cosmic ray muons, plus information about the mechanical structure of the tracker, and initial position uncertainties have been used as input for the alignment procedure. A proof of concept of this alignment strategy is demonstrated using simulated data.