Analytical determination of the two-body gravitational interaction potential at the fourth post-Newtonian approximation

We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing the gravitational interaction of two bodies within the effective one-body formalism. The (nonlogarithmic) coefficient a(5)(nu) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio nu. Its nu-independent part a(5)(0) is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation. Its nu-linear part a(nu) - a(5)(0) is deduced from recent results of Jaranowski and Schafer, and is found to be significantly negative.