Sub-keV Electron Recoil Calibration for Macroscopic Cryogenic Calorimeters using a Novel X-ray Fluorescence Source

Percent-level calibration of cryogenic macro-calorimeters with energy thresholds below 100~eV are crucial for light Dark Matter (DM) searches and reactor neutrino studies based on coherent elastic neutrino-nucleus scattering (CEvNS). This paper presents a novel calibration source based on X-ray fluorescence (XRF) of light elements. It uses a ${}^{55}$Fe source to irradiate a two-staged target arrangement, emitting characteristic emission lines from 677,eV to 6.5,keV. We demonstrate the potential of this new XRF source to calibrate a 0.75 gram CaWO${}_4$ crystal of the NUCLEUS and CRAB experiments. Additionally, we introduce CryoLab, an advanced analysis tool for cryogenic detector data, featuring robust methods for data processing, calibration, and high-level analysis, implemented in MATLAB and HDF5. We also present a phenomenological model for energy resolution, which incorporates statistical contributions, systematic effects, and baseline noise, enabling a novel approach to evaluating athermal phonon collection efficiency in macro-calorimeters based on transition edge sensors (TES).