Rotationally non-invariant aspects of scattering amplitudes with graviton exchange

We consider the s-channel scattering of massive fermion or vector-boson pairs with equal helicities, mediated by a graviton in the linearized Einstein theory. We show that, although in general both spin-2 and spin-0 components are present in the exchanged graviton, there is a special set of reference frames where the spin-0 graviton component vanishes. This is connected to the dependence of the trace of the graviton propagator on the effective dimension of the space-time spanned by the sources. On the other hand, one finds a non-vanishing (Lorentz-invariant) interference of the graviton amplitude with the scalar-exchange amplitude, that in principle could give measurable effects.