Gravitational decay of the Z-boson

We study the decay process of the Z boson to a photon and a graviton. The most general form of the on-shell amplitude, subject to the constraints due to the conservation of the electromagnetic and the energy-momentum tensor, is determined. The amplitude is expressed in terms of three form factors, two of which are CP-odd while one is CP-even. The latter, which is the only non-zero form factor at the one-loop level, is computed in the standard model and the decay rate is determined.