Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

Abstract

We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a "conservative" term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit-shrinking the binary to a pointwhich transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

“…11 The result (3.15) agrees with the non-local action for the 4PN tail term which has been considered in [67] [see Eq. (4.4) there] and investigated in the effective field theory approach [74,75]. Note however that while this contribution was added by hand to the 4PN local action in [67], we have shown here how to 11 For any regular function f (t) tending to zero sufficiently rapidly when t → ±∞ we have…”

“…Once they have been constructed, the equations (2.7) can be order reduced by replacing iteratively all the higher-order accelerations by their expressions coming from the PN equations of motion themselves. The classical Fokker action should be equivalent, in the "tree-level" approximation, to the effective action used by the effective field theory [44,64,74,75].…”

Radiation reaction for spinning bodies in effective field theory. II. Spin-spin effects

“…In a companion paper [4], we reported the resulting radiation-reaction equations of motion to linear order in the spins, which appear at fourth postNewtonian (4PN) order, using the effective field theory (EFT) formalism. At this order conservative contributions are also known using more traditional methods [5] as well as the EFT approach [6,7], encompassing spin-independent [8][9][10][11][12][13][14][15][16][17][18] (see also [19,20]) and spin-dependent terms. 1 See [5,55] for extensive reviews on the postNewtonian expansion, and [56][57][58][59][60][61] for reviews on the EFT approach to the binary problem.…”

Radiation reaction for spinning bodies in effective field theory. I. Spin-orbit effects

“…In other words, in terms of the relative coordinates, At leading order in Newton's constant, the effective action is expressed in terms of Feynman diagrams as ð2:6Þ and yields the following nonconservative piece [19]: The superscript (n) in the multipole moments represents the number of time derivatives. For this paper, the lowest mass-and current-type multipole terms suffice to capture the contributions from the leading order spin effects to radiation reaction, This result is the well-known Burke-Thorne acceleration [61,62] and was derived in the EFT approach in [64,71].…”

“…The effective field theory (EFT) formalism, originally introduced in [15], has readily reproduced many of these calculations, especially in the conservative sector for nonspinning bodies [15][16][17][18][19][20][21]. On the other hand, when spin degrees of freedom are included [22], the EFT framework has increased the knowledge of the gravitational dynamics and emitted power to 3PN order [23][24][25][26][27][28][29][30][31][32][33].…”