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 the upper bound on neutrino-Majoron coupling. We show that the strongest upper bound on the coupling to ν_e comes from the ν_eν_e→J process in the core of a supernova. We also find bounds on diagonal couplings of the Majoron to ν_μ(τ)ν_μ(τ) and on off-diagonal ν_eν_μ(τ) couplings in various regions of the parameter space. We discuss the evaluation of the cross section for four-particle interactions (νν⃗JJ and νJ⃗νJ). We show that these are typically dominated by three-particle subprocesses and do not give new independent constraints.