Precision determination of the track-position resolution of beam telescopes

Beam tests using tracking telescopes are a standard method for determining the spatial resolution of detectors. This requires the precise knowledge of the position resolution of beam tracks reconstructed at the Device Under Test (DUT). A method is proposed which achieves this using a segmented silicon detector with readout with charge digitization. It is found that the DUT spatial resolution for particles with normal incidence is less than 1 $\mu$m for events where clusters consist of two pixels (or strips). Given this accuracy, the residual of the beam track-position at the DUT and the position reconstructed in the DUT provides the beam track-position resolution distribution. The method is developed using simulated events, which are also used to study how to deal with cross-talk, electronics noise, energetic $\delta $-electrons, and incident beams with a few degrees off the normal to the sensor plane. To validate the method, the position resolution of beam tracks reconstructed by the EUDET beam telescope of the DESY II Test Beam Facility is determined using a CMS Phase-2 prototype pixel sensor.