Majorons and supernova cooling

We consider the role of Majoron emission in supernova cooling and its implications for the neutrino mass and lifetime in generic single Majoron models. It is found that, for ${\nu }_{\tau }$ with mass $m$, if the lifetime for the decay ${\nu }_{\tau }\to \mathrm{Majoron}+{\nu }_{e,\mu }$ is shorter than ${10}^{-7\mathrm{}}$ (m/MeV) sec, then Majorons are so strongly trapped by the inverse process that the resulting Majoron luminosity is small enough not to destabilize the observed ${\nu }_e$ pulse from SN 1987A. For ${\nu }_{\tau }$ with a longer lifetime, the Majoron luminosity can be large enough to destroy or significantly shorten the duration of the neutrino pulse. We then find the range of parameters, e.g., the ${\nu }_{\tau }$ mass $m$ and the $B-L$-breaking scale $v$, that is excluded by giving such a large Majoron luminosity. Our results imply that, for $v$ between 1 GeV and 1 TeV, a wide range of $m$ allowed by terrestrial experiments can be excluded in view of the observed ${\nu }_e$, pulse from SN 1987A.