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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:59:22 +0000Simple Recursion Relations for General Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20150311-194335939
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1007/JHEP06(2015)118
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c075k-m0j21Nonrenormalization Theorems without Supersymmetry
https://resolver.caltech.edu/CaltechAUTHORS:20150601-134624745
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}]}
Year: 2015
DOI: 10.1103/PhysRevLett.115.071601
We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w, w¯) = (n − h,n + h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_i can only be renormalized by an operator O_j if w_i ≥ w_j and w¯_i ≥ w¯_j, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dr7bs-jvp76Computing decay rates for new physics theories with FeynRules and MadGraph 5_aMC@NLO
https://resolver.caltech.edu/CaltechAUTHORS:20151106-082017284
Authors: {'items': [{'id': 'Alwall-J', 'name': {'family': 'Alwall', 'given': 'Johan'}}, {'id': 'Duhr-C', 'name': {'family': 'Duhr', 'given': 'Claude'}}, {'id': 'Fuks-B', 'name': {'family': 'Fuks', 'given': 'Benjamin'}}, {'id': 'Mattelaer-O', 'name': {'family': 'Mattelaer', 'given': 'Olivier'}}, {'id': 'Öztürk-D-G', 'name': {'family': 'Öztürk', 'given': 'Deniz Gizem'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}]}
Year: 2015
DOI: 10.1016/j.cpc.2015.08.031
We present new features of the FeynRules and MadGraph 5_aMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any quantum field theory, possibly including higher-dimensional operators. We extend at the same time the conventions of the Universal FeynRules Output (or UFO) format to include decay tables and information on the total widths. We finally provide a set of representative examples of the usage of the new functions of the different codes in the framework of the Standard Model, the Higgs Effective Field Theory, the Strongly Interacting Light Higgs model and the Minimal Supersymmetric Standard Model and compare the results to available literature and programs for validation purposes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gn75c-86p22On-Shell Recursion Relations for Effective Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20151022-121225042
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampf-K', 'name': {'family': 'Kampf', 'given': 'Karol'}}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2016
DOI: 10.1103/PhysRevLett.116.041601
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2r60g-92j88A Periodic Table of Effective Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20161114-161621602
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampk-K', 'name': {'family': 'Kampf', 'given': 'Karol'}, 'orcid': '0000-0003-1096-667X'}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2017
DOI: 10.1007/JHEP02(2017)020
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/t2kee-x9e40Symmetry for Flavor-Kinematics Duality from an Action
https://resolver.caltech.edu/CaltechAUTHORS:20161214-090434989
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}]}
Year: 2017
DOI: 10.1103/PhysRevLett.118.121601
We propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. In this picture, the vanishing soft behavior of amplitudes is a by-product of the Weinberg soft theorem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m0771-36j97Unifying Relations for Scattering Amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20170518-093708530
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Wen-Congkao', 'name': {'family': 'Wen', 'given': 'Congkao'}, 'orcid': '0000-0002-5174-1576'}]}
Year: 2018
DOI: 10.1007/JHEP02(2018)095
We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. Transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tnaz1-w8c77Pions as Gluons in Higher Dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20170918-164427389
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Remmen-G-N', 'name': {'family': 'Remmen', 'given': 'Grant N.'}, 'orcid': '0000-0001-6569-8866'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Wen-Congkao', 'name': {'family': 'Wen', 'given': 'Congkao'}, 'orcid': '0000-0002-5174-1576'}]}
Year: 2018
DOI: 10.1007/JHEP04(2018)129
We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hgq0c-prx17Vector Effective Field Theories from Soft Limits
https://resolver.caltech.edu/CaltechAUTHORS:20180117-160027517
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampk-K', 'name': {'family': 'Kampf', 'given': 'Karol'}, 'orcid': '0000-0003-1096-667X'}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}, {'id': 'Wen-Congkao', 'name': {'family': 'Wen', 'given': 'Congkao'}, 'orcid': '0000-0002-5174-1576'}]}
Year: 2018
DOI: 10.1103/PhysRevLett.120.261602
We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h883z-s7g63Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
https://resolver.caltech.edu/CaltechAUTHORS:20190116-120534227
Authors: {'items': [{'id': 'Bern-Z', 'name': {'family': 'Bern', 'given': 'Zvi'}}, {'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Roiban-R', 'name': {'family': 'Roiban', 'given': 'Radu'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Solon-M-P', 'name': {'family': 'Solon', 'given': 'Mikhail P.'}}, {'id': 'Zeng-Mao', 'name': {'family': 'Zeng', 'given': 'Mao'}, 'orcid': '0000-0002-4741-4038'}]}
Year: 2019
DOI: 10.1103/PhysRevLett.122.201603
We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order and find agreement with known results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9jz6r-2ee23Black Hole Binary Dynamics from the Double Copy and Effective Theory
https://resolver.caltech.edu/CaltechAUTHORS:20190910-111306536
Authors: {'items': [{'id': 'Bern-Z', 'name': {'family': 'Bern', 'given': 'Zvi'}}, {'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Roiban-R', 'name': {'family': 'Roiban', 'given': 'Radu'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Solon-M-P', 'name': {'family': 'Solon', 'given': 'Mikhail P.'}}, {'id': 'Zeng-Mao', 'name': {'family': 'Zeng', 'given': 'Mao'}, 'orcid': '0000-0002-4741-4038'}]}
Year: 2019
DOI: 10.1007/JHEP10(2019)206
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rrv7w-n8c27Hidden conformal invariance of scalar effective field theories
https://resolver.caltech.edu/CaltechAUTHORS:20201202-145220824
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Mangan-James', 'name': {'family': 'Mangan', 'given': 'James'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}]}
Year: 2020
DOI: 10.1103/physrevd.102.125009
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic O(p⁴) vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension D=0. For the case of a quartic O(p⁶) vertex, classical conformal invariance constrains the theory to be the special Galileon in D=−2 dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hggmv-ty549Scattering Amplitudes and Conservative Binary Dynamics at O(G⁴)
https://resolver.caltech.edu/CaltechAUTHORS:20210122-074326668
Authors: {'items': [{'id': 'Bern-Zvi', 'name': {'family': 'Bern', 'given': 'Zvi'}, 'orcid': '0000-0001-9075-9501'}, {'id': 'Parra-Martinez-Julio', 'name': {'family': 'Parra-Martinez', 'given': 'Julio'}, 'orcid': '0000-0003-0178-1569'}, {'id': 'Roiban-Radu', 'name': {'family': 'Roiban', 'given': 'Radu'}}, {'id': 'Ruf-Michael-S', 'name': {'family': 'Ruf', 'given': 'Michael S.'}, 'orcid': '0000-0001-6770-2822'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Solon-Mikhail-P', 'name': {'family': 'Solon', 'given': 'Mikhail P.'}}, {'id': 'Zeng-Mao', 'name': {'family': 'Zeng', 'given': 'Mao'}, 'orcid': '0000-0002-4741-4038'}]}
Year: 2021
DOI: 10.1103/PhysRevLett.126.171601
Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G⁴). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G³) via its relation to the tail effect.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ykjs8-1ge79Leading nonlinear tidal effects and scattering amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20201111-121307251
Authors: {'items': [{'id': 'Bern-Zvi', 'name': {'family': 'Bern', 'given': 'Zvi'}, 'orcid': '0000-0001-9075-9501'}, {'id': 'Parra-Martinez-Julio', 'name': {'family': 'Parra-Martinez', 'given': 'Julio'}, 'orcid': '0000-0003-0178-1569'}, {'id': 'Roiban-Radu', 'name': {'family': 'Roiban', 'given': 'Radu'}}, {'id': 'Sawyer-Eric', 'name': {'family': 'Sawyer', 'given': 'Eric'}, 'orcid': '0000-0003-4144-5607'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}]}
Year: 2021
DOI: 10.1007/JHEP05(2021)188
We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/82g0h-00790Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G⁴)
https://resolver.caltech.edu/CaltechAUTHORS:20220520-231732000
Authors: {'items': [{'id': 'Bern-Zvi', 'name': {'family': 'Bern', 'given': 'Zvi'}, 'orcid': '0000-0001-9075-9501'}, {'id': 'Parra-Martinez-Julio', 'name': {'family': 'Parra-Martinez', 'given': 'Julio'}, 'orcid': '0000-0003-0178-1569'}, {'id': 'Roiban-Radu', 'name': {'family': 'Roiban', 'given': 'Radu'}}, {'id': 'Ruf-Michael-S', 'name': {'family': 'Ruf', 'given': 'Michael S.'}, 'orcid': '0000-0001-6770-2822'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Solon-Mikhail-P', 'name': {'family': 'Solon', 'given': 'Mikhail P.'}}, {'id': 'Zeng-Mao', 'name': {'family': 'Zeng', 'given': 'Mao'}, 'orcid': '0000-0002-4741-4038'}]}
Year: 2022
DOI: 10.1103/physrevlett.128.161103
We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G⁴) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0sq05-d3f54