  We extend the analytical determination of the main radial potential
describing (within the effective one-body formalism) the gravitational
interaction of two bodies beyond the 4th post-Newtonian approximation recently
obtained by us. This extension is done to linear order in the mass ratio by
applying analytical gravitational self-force theory (for a particle in circular
orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant
redshift variable. By using the version of black hole perturbation theory
developed by Mano, Suzuki and Takasugi, we have pushed the analytical
determination of the (linear in mass ratio) radial potential to the 6th
post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In
principle, our analytical method can be extended to arbitrarily high
post-Newtonian orders.
