Neutrinoless double-beta decay search with the LEGEND experiment

Neutrinoless double-beta decay is a nuclear decay, given as $(A,Z) \rightarrow (A, Z+2) +2e^{-}$, with deep consequences for the understanding of our universe. A strong experimental program is underway to search for this transition with many proposed experiments using different technologies. In this article the LEGEND experiment, which uses $^{76}$Ge as the isotope of interest, will be described. We will discuss both the first stage, LEGEND-200, which is now taking data at the Laboratori Nazionali del Gran Sasso of INFN in Italy, and the future stage, LEGEND-1000. LEGEND-200 has analyzed a first sample of data (48.3 kg$\cdot$yr) collected from March 2023 to February 2024 with a background index not far away from its goal of 2$\times$10$^{-4}$ cnts/(keV$\cdot$kg$\cdot$yr). Combining the LEGEND-200 data with those of \textsc{Gerda}\ and \textsc{Majorana Demonstrator}\ one obtains a sensitivity on the half-life of 0$\nu\beta\beta$ decay in $^{76}$Ge of $T_{1/2} > $ 2.8 $\times$ 10$^{26}$ yr at 90\% C.L. and a limit on $T_{1/2} > $ 1.9 $\times$ 10$^{26}$ yr at 90\% C.L.