Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. I. Regularized Lagrangian

Within the framework of the effective field theory approach to the post-Newtonian approximation to general relativity, we report the so-far missing $G^3$ and $G^4$ sectors of the conservative two-body dynamics at fourth perturbative order for nonspinning compact objects. Following the standard procedure, the gravitational interaction is integrated out to obtain a systematic expansion in terms of Feynman graphs. Building on this result and on previously obtained ones, we are able to write the local-in-time regularized Lagrangian at fourth post-Newtonian order, which is in agreement with results previously computed with other methods.

Figure 1

Two-loop master integrals in eq. (12).

Figure 2

Three-loop master integrals in Eq. (13).