The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: Potential contributions

We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post–Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also consider the non–local tail contributions. Further steps towards the complete calculation are discussed. We calculate all but the rational O(ν2) contributions to the bound state energy for circular motion and periastron advance K(Eˆ,j). Comparisons are given to results in the literature.