Measurement of the double-beta decay half-life and search for the neutrinoless double-beta decay of ${}^{48}\mathrm{C}\mathrm{a}$ with the NEMO-3 detector

The NEMO-3 experiment at the Modane Underground Laboratory has investigated the double-$\beta$ decay of ${}^{48}\mathrm{C}\mathrm{a}$. Using $5.25$ yr of data recorded with a $6.99\mathrm{g}$ sample of ${}^{48}\mathrm{C}\mathrm{a}$, approximately $150$ double-$\beta$ decay candidate events have been selected with a signal-to-background ratio greater than $3$. The half-life for the two-neutrino double-$\beta$ decay of ${}^{48}\mathrm{C}\mathrm{a}$ has been measured to be $T^{2\nu}{1/2},=,[6.4, ^{+0.7}{-0.6}{\rm (stat.)} , ^{+1.2}_{-0.9}{\rm (syst.)}] \times 10^{19},{\rm yr}$\mathrm{.}Asearchforneutrinolessdouble-$\beta$decayof$^{48}{\rm Ca}$ yields a null result and a corresponding lower limit on the half-life is found to be $T_{1\mathrm{/}2}^{0\nu }>2.0\times {10}^{22}\mathrm{y}\mathrm{r}$ at $90\mathrm{\%}$ confidence level, translating into an upper limit on the effective Majorana neutrino mass of $<m_{\beta \beta }><6.0-26$ $\mathrm{e}\mathrm{V}$, with the range reflecting different nuclear matrix element calculations. Limits are also set on models involving Majoron emission and right-handed currents.