Track-based alignment for the BESIII CGEM detector in the cosmic-ray test

The Beijing Electron Spectrometer III (BESIII) is a multipurpose detector operating on the Beijing Electron Positron Collider II (BEPCII). After more than ten year's operation, the efficiency of the inner layers of the Main Drift Chamber (MDC) decreased significantly. To solve this issue, the BESIII collaboration is planning to replace the inner part of the MDC with three layers of Cylindrical triple Gas Electron Multipliers (CGEM). The transverse plane spatial resolution of CGEM is required to be 120 $\mu$m or better. To meet this goal, a careful calibration of the detector is necessary to fully exploit the potential of the CGEM detector. In all the calibrations, the detector alignment plays an important role to improve the detector precision. The track-based alignment for the CGEM detector with the Millepede algorithm is implemented to reduce the uncertainties of the hit position measurement. Using the cosmic-ray data taken in 2020 with the two layers setup, the displacement and rotation of the outer layer with respect to the inner layer is determined by a simultaneous fit applied to more than 160000 tracks. A good alignment precision has been achieved that guarantees the design request could be satisfied in the future. A further alignment is going to be performed using the combined information of tracks from cosmic-ray and collisions after the CGEM is installed into the BESIII detector.