We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.
Abstract:We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
We study B --> K(*)l+l- decays (l = e, mu) based on a data sample of 657 x 10(6) BB pairs collected with the Belle detector at the KEKB e+e- collider. We report the differential branching fraction, isospin asymmetry, K* polarization, and the forward-backward asymmetry (A(FB)) as functions of q2 = M(ll)(2)c2. The fitted A(FB) spectrum exceeds the standard model expectation by 2.7 standard deviations. The measured branching fractions are B(B --> K*l+l-) = (10.7(-1.0)(+1.1) +/- 0.9) x 10(-7) and B(B --> Kl+l-) = (4.8(-0.4)(+0.5) +/- 0.3) x 10(-7), where the first errors are statistical and the second are systematic, with the muon to electron ratios R(K*) = 0.83 +/- 0.17 +/- 0.08 and R(K) = 1.03 +/- 0.19 +/- 0.06.
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.