Application of gamma Transition-Edge-Sensor (TES) to 112Sn two-neutrino double electron capture search<bold> </bold>

Double electron capture (DEC) is a rare nuclear decay process in which two orbital electrons are simultaneously captured in the same nucleus. The measurement of its two -neutrino emitting mode (2vDEC) provides a new reference for the calculation of nuclear matrix elements, while the zeroneutrino emitting mode (OvDEC) would demonstrate a violation of lepton number conservation. For Sn-112, the search for DEC to the excited state in Cd-112 has been carried out using a High-Purity Germanium detector and a 112Sn enriched tin sample, but no significant signal has been observed so far. 2vDEC to the ground state in 112Cd has not been performed due to the self-absorption of X-rays and Auger electrons in the tin sample. We propose a novel approach to search for the 2vDEC mode to the ground state in 112Cd using a gamma-ray Transition Edge Sensors (gamma-IESs) with tin absorbers. The calorimetric approach in which the signal would be generated in the detector allows us to detect two X-ray or Auger electrons resulting from the Sn-112 DEC with high energy resolution. The future multi-pixel gamma-IESs increase the target mass and thus the sensitivity. In this proceedings, we demonstrate the 2vDEC search with this approach. The preliminary results of our search for the (1125)n 2vDEC to the ground state in 112Cd with 90 hours, four y-TESs data, and the future prospects are presented.