Effects of misalignment on response uniformity of SiPM-on-tile technology for highly granular calorimeters

The SiPM-on-tile technology, consisting of plastic scintillator tiles with typical sizes of a few cm$^2$ mounted on top of SiPMs, has been developed within the CALICE collaboration to enable automatized mass production of active elements for scintillator-based highly granular calorimeters. We present a study of the impact of misalignment of the scintillator tile with respect to the photon sensor on the response uniformity and on the absolute light yield for square, hexagonal and rhomboidal scintillator tiles of different sizes. A misalignment results in the formation of a dipole asymmetry of the spatial distribution of the light yield, with a magnitude that scales linearly with the size of the displacement, while the average light yield over the full active area of the tile is not affected. These results provide guidance for the definition of tolerances for the production and assembly of large calorimeter systems, showing that an alignment precision of approximately 500 $\mu$m or better allows to limit the impact to acceptable levels.