Search for Majoron-like particles with CUPID-0

We present the first search for the Majoron-emitting modes of the neutrinoless double $\ensuremath{\beta}$ decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}{\ensuremath{\chi}}_{0}$) using scintillating cryogenic calorimeters. We analyzed the CUPID-0 Phase I data using a Bayesian approach to reconstruct the background sources activities, and evaluate the potential contribution of the $^{82}\mathrm{Se}$ $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}{\ensuremath{\chi}}_{0}$. We considered several possible theoretical models which predict the existence of a Majoron-like boson coupling to the neutrino. The energy spectra arising from the emission of such bosons in the neutrinoless double $\ensuremath{\beta}$ decay have spectral indices $n=1$, 2, 3, or 7. We found no evidence of any of these decay modes, setting a lower limit (90% of credibility interval) on the half-life of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{23}\text{ }\text{ }\mathrm{yr}$ in the case of $n=1$, $3.8\ifmmode\times\else\texttimes\fi{}{10}^{22}\text{ }\text{ }\mathrm{yr}$ for $n=2$, $1.4\ifmmode\times\else\texttimes\fi{}{10}^{22}\text{ }\text{ }\mathrm{yr}$ for $n=3$ and $2.2\ifmmode\times\else\texttimes\fi{}{10}^{21}\text{ }\text{ }\mathrm{yr}$ for $n=7$. These are the best limits on the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}{\ensuremath{\chi}}_{0}$ half-life of the $^{82}\mathrm{Se}$, and demonstrate the potentiality of the CUPID-0 technology in this field.