In supergravity models with low supersymmetry-breaking scale, the gravitinos can be superlight, with mass in the ${10}^{-6}\mathrm{eV}$ to a few keV range. In such a case, gravitino emission provides a new cooling mechanism for protoneutron stars and therefore can provide constraints on the mass of a superlight gravitino. This happens because the coupling to matter of superlight gravitinos is dominated by its Goldstino component, whose coupling to matter is inversely proportional to the scale of supersymmetry breaking and increases as the gravitino mass decreases. Present observations therefore provide lower limits on the gravitino mass. Using the recently revised Goldstino couplings, we find that the two dominant processes in supernova cooling are $e^{+}{e}^{-}\to \tilde{G}\tilde{G}$ and $\gamma {+e}^{-}\to e^{-}\tilde{G}\tilde{G}.$ They lead to a lower limit on the supersymmetry-breaking scale ${\Lambda }_S$ from 160 to 500 GeV for core temperatures 30 to 60 MeV and electron chemical potentials 200 to 300 MeV. The corresponding lower limits on the gravitino mass are 0.6 to $6\times {10}^{-6}\mathrm{eV}.$

• Received 15 August 1997

DOI:https://doi.org/10.1103/PhysRevD.57.578