Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

摘要

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation ofgeneral relativity has been determined previously. However two ambiguity parameters associated withinfrared (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed bycomparison with gravitational self-force (GSF) calculations of the conserved energy and periastronadvance for circular orbits in the test-mass limit. In the present paper together with a companion paper,we determine both these ambiguities from first principle, by means of dimensional regularization. Ourcomputation is thus entirely defined within the dimensional regularization scheme, for treating at oncethe IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from theEinstein-Hilbert part of the action and from the nonlocal tail term in arbitrary dimensions, which resolvethe ambiguities.