Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:math> decay half-life and search for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>0</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:math> decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Cd</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>116</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> with the NEMO-3 detector

The NEMO-3 experiment measured the half-life of the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay and searched for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{116}\mathrm{Cd}$. Using 410 g of $^{116}\mathrm{Cd}$ installed in the detector with an exposure of 5.26 y, ($4968\ifmmode\pm\else\textpm\fi{}74$) events corresponding to the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{116}\mathrm{Cd}$ to the ground state of $^{116}\mathrm{Sn}$ have been observed with a signal to background ratio of about 12. The half-life of the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay has been measured to be ${T}_{1/2}^{2\ensuremath{\nu}}=[2.74\ifmmode\pm\else\textpm\fi{}0.04(\text{stat})\ifmmode\pm\else\textpm\fi{}0.18(\text{syst})]\ifmmode\times\else\texttimes\fi{}1{0}^{19}\text{ }\text{ }\mathrm{y}$. No events have been observed above the expected background while searching for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. The corresponding limit on the half-life is determined to be ${T}_{1/2}^{0\ensuremath{\nu}}\ensuremath{\ge}1.0\ifmmode\times\else\texttimes\fi{}1{0}^{23}\text{ }\text{ }\mathrm{y}$ at the 90% C.L. which corresponds to an upper limit on the effective Majorana neutrino mass of $⟨{m}_{\ensuremath{\nu}}⟩\ensuremath{\le}1.4--2.5\text{ }\text{ }\mathrm{eV}$ depending on the nuclear matrix elements considered. Limits on other mechanisms generating $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay such as the exchange of R-parity violating supersymmetric particles, right-handed currents and majoron emission are also obtained.