More on Violation of Angular-Momentum Selection Rules in Quantum Gravity

In a recent paper, we noticed that, in the s-channel scattering mediated by a graviton in the linearized Einstein theory, angular momentum seems not to be conserved in the graviton coupling to massive matter fields, due to the presence of a scalar component in the partial-wave expansion of the relevant amplitudes. The present Letter answers to some criticism by Han and Willenbrock, claiming that there is no problem in propagating a scalar component through a graviton exchange. We show explicitly that the partial-wave decomposition of the scattering amplitude contrasts with the rotation-group representations propagating through the graviton exchange in the considered processes. This phenomenon is crucially connected to the critical dependence of the trace of the graviton propagator on the "effective" dimension of the problem.