Final results on ${}^\mathbf 82 \hbox {Se}$ double beta decay to the ground state of ${}^\mathbf 82 \hbox {Kr}$ 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 $T_{\smash {1/2}}^{2\nu } \!=\! \left[ 9.39 \pm 0.17\left( \text{ stat }\right) \pm 0.58\left( \text{ syst }\right) \right] \times 10^{19}$  y under the single-state dominance hypothesis for this nuclear transition. The corresponding nuclear matrix element is $\left| M^{2\nu }\right| = 0.0498 \pm 0.0016$ . 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 $T_{1/2}^{0\nu } > 2.5 \times 10^{23} \,\text{ y } \,(90\%\,\text{ C.L. })$ for the light neutrino exchange mechanism leads to a constraint on the effective Majorana neutrino mass of $\langle m_{\nu } \rangle < \left( 1.2{-}3.0\right) \,\text{ eV }$ , 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.