One-loop n-point helicity amplitudes in (self-dual) gravity

We present an ansatz for all one-loop amplitudes in pure Einstein gravity f or which the n external gravitons have the same outgoing helicity. These lo op amplitudes, which are rational functions of the momenta, also arise in t he quantization of self-dual gravity in four-dimensional Minkowski space. O ur ansatz agrees with explicit computations via D-dimensional unitarity cut s for n less than or equal to 6. It also has the expected analytic behavior , for all n, as a graviton becomes soft, and as two momenta become collinea r. The gravity results are closely related to analogous amplitudes in (self -dual) Yang-Mills theory. (C) 1998 Elsevier Science B.V. All rights reserve d.