Final results on ${}^{\mathbf{\text{82}}}$Se double beta decay to the ground state of ${}^{\mathbf{\text{82}}}$Kr from the NEMO-3 experiment

Using data from the NEMO-3 experiment, we have measured the two-neutrino double beta decay ($2\nu \beta \beta$) half-life of ${}^{82}$Se as $T_{1/2}^{2\nu} = \left[ 9.39 \pm 0.17,\left(\mbox{stat}\right) \pm 0.58,\left(\mbox{syst}\right)\right] \times 10^{19}$ y under the single-state dominance hypothesis for this nuclear transition. The corresponding nuclear matrix element is $\mid M^{2\nu }\mid =0.0498\pm 0.0016$. In addition, a search for neutrinoless double beta decay ($0\nu \beta \beta$) using 0.93 kg of ${}^{82}$Se observed for a total of 5.25 y has been conducted and no evidence for a signal has been found. The resulting half-life limit of $T_{1/2}^{0\nu} > 2.5 \times 10^{23} ,\mbox{y} ,(90%,\mbox{C.L.})$ for the light neutrino exchange mechanism leads to a constraint on the effective Majorana neutrino mass of $⟨m_{\nu }⟩<(1.2-3.0)eV$, where the range reflects $0\nu \beta \beta$ nuclear matrix element values from different calculations. Furthermore, constraints on lepton number violating parameters for other $0\nu \beta \beta$ mechanisms, such as right-handed currents, majoron emission and R-parity violating supersymmetry modes have been set.