Bounds on the Coupling of the Majoron to Light Neutrinos from Supernova Cooling

We explore the role of Majoron ($J$) emission in the supernova cooling process, as a source of upper bound on neutrino-Majoron coupling. We show that the strongest upper bound on the coupling to ${\nu }_e$ comes from the ${\nu }_e{\nu }_e\to J$ process in the core of a supernova. We also find bounds on diagonal couplings of the Majoron to ${\nu }_{\mu (\tau )}{\nu }_{\mu (\tau )}$ and on off-diagonal ${\nu }_e{\nu }_{\mu (\tau )}$ couplings in various regions of the parameter space. We discuss the evaluation of the cross-section for four-particle interactions ($\nu \nu \to JJ$ and $\nu J\to \nu J$). We show that these are typically dominated by three-particle sub-processes and do not give new independent constraints.