We present the first performance results obtained with microwave multiplexed Transition Edge Sensors prototypes specifically designed for the HOLMES experiment, a project aimed at directly measuring the electron neutrino mass through the calorimetric measurement of the Ho electron capture spectrum. The detectors required for such an experiment feature a high energy resolution at the Q–value of the transition, around 2.8 keV, and a fast response time combined with the compatibility to be multiplexed in large arrays in order to collect a large statistics while keeping the pile-up contribution as small as possible. In addition, the design has to be suitable for future ion-implantation of Ho. The results obtained in these tests allowed us to identify the optimal detector design among several prototypes. The chosen detector achieved an energy resolution of (4.5 ± 0.3) eV on the chlorine K line, at 2.6 keV, obtained with an exponential rise time of 14 us. The achievements described in this paper pose a milestone for the HOLMES detectors, setting a baseline for the subsequent developments, aiming to the actual ion-implantation of the Ho nuclei. In the first section the HOLMES experiment is outlined along with its physics goal, while in the second section the HOLMES detectors are described; the experimental set-up and the calibration source used for the measurements described in this paper are reported in Sects. 3 and 4, respectively; finally, the details of the data analysis and the results obtained are reported in Sect. 6
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