  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.
