Final results on the $0\nu\beta\beta$ decay half-life limit of $^{100}$Mo from the CUPID-Mo experiment

The CUPID-Mo experiment to search for 0$\nu\beta\beta$ decay in $^{100}$Mo has been recently completed after about 1.5 years of operation at Laboratoire Souterrain de Modane (France). It served as a demonstrator for CUPID, a next generation 0$\nu\beta\beta$ decay experiment. CUPID-Mo was comprised of 20 enriched Li$_2$$^{100}$MoO$_4$ scintillating calorimeters, each with a mass of $\sim$ 0.2 kg, operated at $\sim$20 mK. We present here the final analysis with the full exposure of CUPID-Mo ($^{100}$Mo exposure of 1.47 kg$\times$yr) used to search for lepton number violation via 0$\nu\beta\beta$ decay. We report on various analysis improvements since the previous result on a subset of data, reprocessing all data with these new techniques. We observe zero events in the region of interest and set a new limit on the $^{100}$Mo 0$\nu\beta\beta$ decay half-life of $T^{0\nu}_{1/2} > 1.8 \times 10^{24}$ year (stat.+syst.) at 90% CI. Under the light Majorana neutrino exchange mechanism this corresponds to an effective Majorana neutrino mass of $\left<m_{\beta \beta}\right> < (0.28$--$0.49)$ eV, dependent upon the nuclear matrix element utilized.