Figure 1

Feynman diagrams that give the leading Newtonian interaction. They are of order $L{v}^0$. Actually, the self-energy diagrams (b) and (c) give a vanishing contribution after doing dimensional regularization. Solid lines represent particle worldlines and dashed lines the potential graviton propagator (a13). Dots are point-particle vertices. In these diagrams they are $V_{\mu \nu }^{(1)}$ in (a36). Note that loops closed by a heavy particle worldline are not quantum and contribute to tree-level results (i.e., we have no integration over the particle momentum). Quantum loop corrections would correspond to diagrams with extra powers of $\hslash /L\ll 1$, i.e., with graviton loops. (The reader interested in quantum corrections to the gravitational interaction between two bodies can see 38, 39, 40 and references therein).Reuse & Permissions

Figure 2

Feynman diagrams for the Einstein-Infeld-Hoffmann correction to the Newton interaction. They are of order $L{v}^2$. Only (internal) potential gravitons contribute as mediators of the interaction.Reuse & Permissions

Figure 3

Feynman diagrams for the coupling between the NR source and the radiation gravitons, up to leading order in $v$ where radiation emission occurs. Diagram (a) is of order $\sqrt{L}{v}^{(d-3)/2}$, diagram (b) is $\mathcal{O}(\sqrt{L}{v}^{(d-1)/2})$, and (c)–(e) are order $\sqrt{L}{v}^{(d+1)/2}$. Only external radiation gravitons, represented by wavy lines, describe the radiated waves.Reuse & Permissions

Figure 4

Self-energy diagram whose imaginary contribution gives the quadrupole formula for the radiated power in the form of gravitational waves by an NR system. The double solid lines represent the NR particles. In the low energy ClEFT describing the coupling of the particles to the radiated gravitons, length scales smaller than the orbital distance cannot be resolved. This is pictorially emphasized in this diagram by drawing the particle lines close to each other. This diagram is to be understood as a standard self-energy diagram: at a certain point in the past the system radiates a graviton [described by (4.14)] which is then absorbed back in the future. The amplitude for this process is complex. Its imaginary part encodes the information on the radiated energy through gravitational waves that propagates to the asymptotic region. Again, this is a tree-level diagram since the loop is closed by heavy particle worldlines whose momenta are not integrated.Reuse & Permissions