Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses

Abstract

We compute the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop (and 5th post-Newtonian) approximation to the harmonic coordinates effective action in a direct calculation. The computation is performed using effective field methods based on Feynman diagrams in momentum-space in $d=3-2\epsilon$ space dimensions. We also reproduce the previous results including the 4th post-Newtonian order.

15 pages, 4 figures. Journal version plus corrected typographical errors in formula for master integral M_{72}