Supernovae and Weinberg's Higgs Portal Dark Radiation and Dark Matter

The observed burst duration and energies of the neutrinos from Supernova 1987A strongly limit the possibility of any weakly-interacting light particle species being produced in the proto-neutron star (PNS) core and leading to efficient energy loss. We reexamine this constraint on Weinberg's Higgs portal model, in which the dark radiation particles (the Goldstone bosons) and the dark matter candidate (a Majorana fermion) interact with Standard Model (SM) fields solely through the mixing of the SM Higgs boson and a light Higgs boson. In order for the Goldstone bosons to freely stream out of the PNS core region, the Higgs portal coupling has to be about a factor of $4$--$9$ smaller than the current collider bound inferred from the SM Higgs invisible decay width. We find that in the energy loss rate calculations, results obtained by using the one-pion exchange (OPE) approximation and the SP07 global fits for the nucleon-nucleon total elastic cross section differ only by a factor $\lesssim 3$. The SN 1987A constraints surpass those set by laboratory experiments or by the energy loss arguments in other astrophysical objects such as the gamma-ray bursts, even with other nuclear uncertainties taken into account. Furthermore, the SN 1987A constraints are comparable to bounds from the latest dark matter direct search for low-mass WIMPs ($\lesssim 10~\Gev$.)