S-matrix for s-wave gravitational scattering

In the s-wave approximation the 4d Einstein gravity with scalar fields can be reduced to an effective 2d dilaton gravity coupled non-minimally to the matter fields. We study the leading order (tree level) vertices. The 4-particle matrix element is calculated explicitly. It is interpreted as scattering with formation of a virtual black hole state. As one novel feature we predict the gravitational decay of s-waves.