Weak interactions of a light gravitino: A lower limit on the gravitino mass from the decay ψ→gravitino + antiphotino

The massive gravitino of spontaneously-broken locally supersymmetric theories may well be very light, leading to a mixing between weak and gravitational interactions. Particularly interesting is the photon coupling to a gravitino-antiphotino pair, with a vertex factor ($\text{κ/m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>\surd 6</mtext>}}\text{) γ}{}^{\mathrm{\mu }}\text{q}{}^2$: a one-photon exchange with ordinary fermions is equivalent to a local four-fermion interaction. From the upper limit on the decay ψ → gravitino + antiphotino we get a lower limit ～ 10^?8 eV/c² on the gravitino mass.