Graviton scattering amplitudes in M theory

We compute graviton scattering amplitudes in M theory using Feynman rules for a scalar particle coupled to gravity in eleven dimensions. The processes that we consider describe the single graviton exchange and the double graviton exchange, that in M~atrix! theory correspond to the v/r and v/r term, respectively. We argue that the v/r term appearing in M~atrix! theory at two loops can be obtained from the covariant eleven-dimensional four-graviton amplitude. Finally, we calculate the v/r term appearing at two loops in M~atrix! theory. It has been previously conjectured that this term is related to a four graviton scattering amplitude involving the R vertex of M theory. @S0556-2821~98!01310-1#