Alignment of pixel sensors in ATLAS Forward Proton detectors

The ATLAS Forward Proton (AFP) detector system consists of Roman pots located on both sides at a distance of approximately 205 m and 217 m from the interaction point in the very forward region of the ATLAS detector. The AFP detector is intended to expand the physics reach of ATLAS by tagging and measuring very forward protons. One of the important parts of this detector system, the 3D Silicon Tracker (SiT) records the hits of the protons that remained intact after the collision. These hits are then reconstructed as a cluster, a track, and a proton, respectively. Alignment of the pixel sensors (inter-plane alignment) in the AFP detector, which is the shift and rotation of each plane in a Roman pot, is required to more precisely determine the properties of the reconstructed objects. In this study, a method that calculates the residuals of cluster and track positions for use in inter-plane alignment is introduced. Only the alignment parameters of the x- and y-direction offsets ($\mathrm{\delta x}$ and $\mathrm{\delta y}$) and the rotation angle ($\mathrm{\alpha}$) about the z-axis for each SiT plane are considered. The values for the alignment parameters ($\mathrm{\delta x}$, $\mathrm{\delta y}$, $\mathrm{\alpha}$) after 30 iterations are calculated, and they are convergent as expected.