  In a previous paper we presented the renormalization of Einstein-Hilbert
gravity under inclusion of higher derivative terms and proposed a projection
down to the physical state space of Einstein-Hilbert. In the present paper we
describe this procedure in more detail via decomposing the original double-pole
field $h^{\mu\nu}$ in the bilinear field sector into a massless and a massive
spin two field. Those are associated with the poles at zero mass resp. at
non-zero mass of $h$ in the tree approximation. We show that the massive fields
have no poles in higher orders hence do not correspond to particles. $S$-matrix
unitarity is violated only in tree approximation. On the way to these results
we derive finiteness properties which are valid in the Landau gauge. Those
simplify the renormalization group analysis of the model considerably. We also
establish a rigid Weyl identity which represents a proper substitute for a
Callan-Symanzik equation in flat spacetime.
