Effective field theory calculation of second post-Newtonian binary dynamics

Abstract

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second Post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second Post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.

Figures (6)

• Figure 1: Order $G$ topology. The single solid line denotes a generic graviton field, either $\phi$, $A_i$, or $\sigma_{ij}$, and double solid lines denote the worldlines of the binary constituents.
• Figure 2: Topologies at order $G^2$.
• Figure 3: Topologies at order $G^3$.
• Figure 4: Order $Gv^4$ diagrams at 2PN. Here the dashed, wavy, and double wavy lines, represent the $\phi$, $A_i$, and $\sigma_{ij}$ fields, respectively. A cross denotes a propagator insertion.
• Figure 5: Order $G^2v^2$ diagrams at 2PN.