The SIDDHARTA-2 calibration method for high precision kaonic atoms X-ray spectroscopy measurements

The SIDDHARTA-2 experiment at the DA$\Phi$NE collider aims to perform the first kaonic deuterium X-ray transitions to the fundamental level measurement, with a systematic error at the level of a few eV. To achieve this challenging goal the experimental apparatus is equipped with 384 Silicon Drift Detectors (SDDs) distributed around its cryogenic gaseous target. The SDDs developed by the SIDDHARTA-2 collaboration are suitable for high precision kaonic atoms spectroscopy, thanks to their high energy and time resolutions combined with their radiation hardness. The energy response of each detector must be calibrated and monitored to keep the systematic error, due to processes such as gain fluctuations, at the level of 2-3 eV. This paper presents the SIDDHARTA-2 calibration method which was optimized during the preliminary phase of the experiment in the real background conditions of the DA$\Phi$NE collider, which is a fundamental tool to guarantee the high precision spectroscopic performances of the system over long periods of data taking, as that required for the kaonic deuterium measurement.