scholarly journals Leading nonlinear tidal effects and scattering amplitudes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Zvi Bern ◽  
Julio Parra-Martinez ◽  
Radu Roiban ◽  
Eric Sawyer ◽  
Chia-Hsien Shen
Keyword(s):  
Scattering Amplitudes ◽  
Effective Field Theory ◽  
Effective Field ◽  
Higher Dimension ◽  
Tidal Effects ◽  
Position Space ◽  
Spinning Particle ◽  
Tidal Deformations ◽  
Higher Order Corrections ◽  
Double Copy

Abstract 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.

scholarly journals The EFT-hedron

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Nima Arkani-Hamed ◽  
Tzu-Chen Huang ◽  
Yu-tin Huang
Keyword(s):  
Scattering Amplitudes ◽  
Effective Field Theory ◽  
Systematic Investigation ◽  
Effective Field ◽  
Low Energy ◽  
Boundary Structure ◽  
Higher Dimension ◽  
Particle Scattering ◽  
Totally Positive ◽  
Positive Structure

Abstract We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden “totally positive” structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the “EFT-hedron”. We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.

scholarly journals EFT anomalous dimensions from the S-matrix

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Joan Elias Miró ◽  
James Ingoldby ◽  
Marc Riembau
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Form Factors ◽  
Effective Field ◽  
Higher Dimension ◽  
Powerful Method ◽  
Loop Contribution ◽  
Anomalous Dimensions ◽  
S Matrix ◽  
The Standard Model

Abstract We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.

scholarly journals Yang-Mills observables: from KMOC to eikonal through EFT

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Leonardo de la Cruz ◽  
Andres Luna ◽  
Trevor Scheopner
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Effective Field Theory ◽  
Effective Field ◽  
Direct Integration ◽  
Spinning Particles ◽  
Yang Mills ◽  
Domain Of Applicability

Abstract We obtain a conservative Hamiltonian describing the interactions of two charged bodies in Yang-Mills through $$ \mathcal{O}\left({\alpha}^2\right) $$ O α 2 and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory (EFT) to consider color-charged objects. These results are checked against the direct integration of the observables in the Kosower-Maybee-O’Connell (KMOC) formalism. At the order we consider we find that the linear and color impulses in a scattering event can be concisely described in terms of the eikonal phase, thus extending the domain of applicability of a formula originally proposed in the context of spinning particles.

Effective field theory with genuine many-body forces and tidal effects on neutron stars

2019 ◽  
Vol 340 (1-3) ◽  
pp. 209-212
Author(s):  
M. Razeira ◽  
D. Hadjimichef ◽  
M. V. T. Machado ◽  
F. Köpp ◽  
G. Volkmer ◽  
...  
Keyword(s):  
Field Theory ◽  
Neutron Stars ◽  
Effective Field Theory ◽  
Effective Field ◽  
Many Body ◽  
Tidal Effects ◽  
Body Forces

scholarly journals Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dimitrios Kosmopoulos ◽  
Andres Luna
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Scattering Amplitudes ◽  
Effective Field Theory ◽  
Effective Field ◽  
Spin Hamiltonian ◽  
Minimal Coupling ◽  
Spinning Bodies

Abstract We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $$ \mathcal{O} $$ O (G2) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in [1] that relates the impulse and spin kick in a scattering event to the eikonal phase.

scholarly journals Spinning black hole binary dynamics, scattering amplitudes, and effective field theory

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Zvi Bern ◽  
Andres Luna ◽  
Radu Roiban ◽  
Chia-Hsien Shen ◽  
Mao Zeng
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Scattering Amplitudes ◽  
Effective Field Theory ◽  
Effective Field ◽  
Black Hole Binary

scholarly journals Post-Minkowskian effective field theory for conservative binary dynamics

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Gregor Kälin ◽  
Rafael A. Porto
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Classical Limit ◽  
Binary Systems ◽  
Effective Field ◽  
Feynman Diagrams ◽  
Scattering Data ◽  
Tidal Effects ◽  
Love Numbers ◽  
The One

Abstract We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1, 2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1, 2], obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude in Cheung et al. [3]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [3] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

scholarly journals EFFECTIVE FIELD THEORY OF A LOCALLY NONCOMMUTATIVE SPACE–TIME AND EXTRA DIMENSIONS

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2613-2633 ◽  
Author(s):  
B. MIRZA ◽  
M. ZAREI
Keyword(s):  
Effective Field Theory ◽  
Extra Dimensions ◽  
Effective Field ◽  
Point Of View ◽  
Effective Theory ◽  
Noncommutative Space ◽  
Higher Dimension ◽  
Full Theory ◽  
Energy Theory ◽  
Effective Theories

We assume that the noncommutativity starts to be visible continuously from a scale ΛNC. According to this assumption, a two-loop effective action is derived for noncommutative ϕ4 and ϕ3 theories from a Wilsonian point of view. We show that these effective theories are free of UV/IR mixing phenomena. We also investigate the positivity constraint on coefficients of higher dimension operators present in the effective theory. This constraint makes the low energy theory to be UV completion of a full theory. Finally, we discuss noncommutativity and extra dimensions. In our effective theories formulated on noncommutative extra dimensions, if the campactification scale Λc is less than the scale ΛNC, the theory will not suffer from UV/IR mixing.

scholarly journals N3LO gravitational quadratic-in-spin interactions at G4

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Michèle Levi ◽  
Andrew J. McLeod ◽  
Matthew von Hippel
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Linear Order ◽  
Effective Field ◽  
Compact Objects ◽  
Spin Orbit ◽  
Spinning Particle ◽  
Transcendental Numbers ◽  
Spin Interactions ◽  
First Time

Abstract We compute the N3LO gravitational quadratic-in-spin interactions at G4 in the post-Newtonian (PN) expansion via the effective field theory (EFT) of gravitating spinning objects for the first time. This result contributes at the 5PN order for maximally-spinning compact objects, adding the spinning case to the static sector at this PN accuracy. This sector requires extending the EFT of a spinning particle beyond linear order in the curvature to include higher-order operators quadratic in the curvature that are relevant at this PN order. We make use of a diagrammatic expansion in the worldline picture, and rely on our recent upgrade of the EFTofPNG code, which we further extend to handle this sector. Similar to the spin-orbit sector, we find that the contributing three-loop graphs give rise to divergences, logarithms, and transcendental numbers. However, in this sector all of these features conspire to cancel out from the final result, which contains only finite rational terms.

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