A study of neutrinoless double electron capture in ${}^{40}$Ca from the AMoRE experiment

The search for neutrinoless double electron capture ($0\nu 2\mathrm{E}\mathrm{C}$) provides a sensitive probe of lepton-number violation and the Majorana nature of neutrinos. We investigate the $0\nu 2\mathrm{E}\mathrm{C}$ decay of ${}^{40}$Ca using cryogenic detectors equipped with metallic magnetic calorimeters in the AMoRE-I experiment. The analysis is based on a physics dataset corresponding to a total exposure of 7.32 kg$\cdot$yr from thirteen ${}^{40}$Ca${}^{100}$MoO${}_4$ crystals. No significant excess is observed, and a lower limit on the half-life is obtained as $T_{1\mathrm{/}2}^{0\nu }>1.7\times {10}^{22}$ yr at 90$\mathrm{\%}$ confidence level. An improved sensitivity is expected for the upcoming AMoRE-II experiment. These results demonstrate the potential of CaMoO${}_4$ detectors to explore rare decay processes beyond the primary ${}^{100}$Mo $0\nu \beta \beta$ search program.