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 a₅(ν) measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio ν. Its ν-independent part a₅(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 ν-linear part a₅(ν)-a₅(0) is deduced from recent results of Jaranowski and Sch\"afer, and is found to be significantly negative.