A new back-propagation method for the CMS GEM chamber alignment with six misalignment parameters

The next phase of high luminosity LHC (HL-LHC) foresees and increases the instantaneous luminosity in order to extend the discovery potential of the detector. In order to meet the increased particle rates and to ensure a robust and redundant system, CMS is adding new detector layers in the forward region of the muon system along with other upgrades. The endcap regions will be equipped with Gas Electron Multiplier (GEM) detectors and improved Resistive Plate Chambers (iRPC). The first of three GEM detector systems (called GE1/1) has been already installed and will operate during Run 3 of LHC starting in 2022. The alignment of the new detector is mandatory for correct muon transverse momentum assignment, thus for muon triggering and reconstruction. We report the status of a newly developed back-propagation method for GEM alignment to reduce the muon momentum dependence due to the multiple scatterings, compared to the standard alignment technique using muon tracks in the CMS tracker system. This new method with six misalignment parameters, 6DOF alignment, significantly improves the accuracies on relative alignments between GEM and CSC chambers for cosmic ray muons, compared to the 3DOF alignment (DP-2022/027).