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Supernova Bounds on Weinberg's Goldstone Bosons

Recently, Weinberg proposed a scenario where Goldstone bosons may be masquerading as fractional cosmic neutrinos. We calculate the energy loss rates through the emission of these Goldstone bosons in a post-collapse supernova core. Invoking the well established emissivity bound from the Supernova 1987A observations and simulations, we find that nuclear bremsstrahlung processes can notably impose a bound on the Goldstone boson coupling to the Standard Model Higgs, $g$, dependent on the mass of the associated radial field, $m_r$. For $m_r$ large enough compared with the temperature in the post-collapse supernova core, our bound is $|g| \lesssim 0.011\, (m_r / 500~{\rm MeV})^2$, very competitive to that derived from collider experiments.