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Results for “SCATTERING AMPLITUDES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗
DOE OSTI2016

Miracles in Scattering Amplitudes: from QCD to Gravity

The goal of my research project "Miracles in Scattering Amplitudes: from QCD to Gravity" involves deepening our understanding of gauge and gravity theories by exploring hidden structures in scattering amplitudes and using these rich structures as much as possible to aid practical calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗
DOE OSTI2024

Gravitational self force from scattering amplitudes in curved space

Abstract We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with massmorbiting in the background spacetime induced by a heavy gravitational source with massM. Observables are organized as an expansion inm/Mto all orders inG— the gravitational self-force expansion. An essential component of our analysis is the backreaction of the heavy source which we capture by including the associated light degrees of freedom. As illustration we consider a Schwarzschild background and verify geodesic motion as well as the first-order self-force correction to two-body scattering through$$\mathcal{O}$$(G 3 ). Amplitudes in curved space offer several advantages, and further developments along these lines may advance the computation of gravitational-wave signals for extreme-mass-ratio inspirals.

Physics↗
NASA NTRS1993

Strong-field cyclotron scattering. I - Scattering amplitudes and natural line width

The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold et al. (1982) and of Sokolov and Ternov (1968), which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson and Lippmann (1949) are not. In addition, it is shown that the Breit-Wigner broadening approximation E tends to E - i(Gamma)/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter.

Graziani, Carlo↗
DOE OSTI2025

QCD Predictions for Physical Multimeson Scattering Amplitudes

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of 𝜋 + and 𝐾 + , at a lattice spacing 𝑎 = 0.063 fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for 𝜋 + ⁢𝐾 + and 2⁢𝐾 + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

hadron-hadron interactions↗
DOE OSTI2014

Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4 $ SYM and 3d ABJM

Scattering amplitudes in 4d N=4 super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space. Here, after a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations. A similar strategy allows us to derive a new Grassmannian integral for 3d N = 6 ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data. The result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for N = 4 SYM.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗
DOE OSTI2021

Scattering amplitudes for all masses and spins

We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin Sparticles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called “spinning polynomials”. Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin cannot be “elementary”. The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can’t be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g - 2) as well as the beta function and rational terms in QCD. “Off-shell” observables like correlation functions and form-factors can be thought of as scattering amplitudes with external “probe” particles of general mass and spin, so all these objects — amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Determination of crossing-symmetric π π scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD

Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the σ , leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice-determined π π partial-wave scattering amplitudes with isospin–0,1,2. We will show that only certain combinations of amplitude parametrizations satisfy all constraints, and that when we restrict to these, the σ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained σ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Scattering Amplitudes in a Neighborhood of Limit Rays in Short-Wave Diffraction by Elongated Bodies of Revolution

In the paper, diffraction problems of a plane wave by smooth, convex, and elongated bodies of revolution are considered within the framework of short-wave approximation (axially symmetric cases). The scattering amplitudes are calculated in the direction of limit rays, and the influence of the elongation of the scatterers on the amplitudes behavior is investigated. Mathematical techniques of our approach are based on the Green’s formulas in the exterior of the scatterers and numerical calculations of the wave field current in the boundary layers in the vicinity of the light-shadow zone. It is established that the elongation of axially symmetric bodies relatively weakly affects the scattering amplitudes of the short-wave asymptotics. The main contribution to the amplitudes is made by the solution of the 2D diffraction problem by a convex, smooth curve in the cross section of the scatterers by a plane containing the rotation axis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Energy-Dependent $π^+π^+π^+$ Scattering Amplitude from QCD

Focusing on three-pion states with maximal isospin ($π^+π^+π^+$), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. Furthermore, to fully implement the latter, we solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Hansen and Sharpe derived a relation between the scattering amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the divergence-free $K$ matrix and denoted $\mathcal K_{df,3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{df,3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the relation between $\mathcal K_{df,3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{df,3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{df,3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Extracting scattering amplitudes for arbitrary two-particle systems with one-particle left-hand cuts via lattice QCD

We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method first relates the finite-volume spectrum to an infinite-volume short-range quantity, denoted ${\mathcal{M}}_0$, and then relates the latter to the physical scattering amplitudes via known integral equations. The derivation of both relations is performed using all-orders perturbation theory and is exact up to neglected exponentially suppressed volume dependence. The relations hold for arbitrary two-particle systems with any number of coupled channels, non-identical and non-degenerate particles, and any intrinsic spin.

algorithms↗
DOE OSTI2022

The SAGEX review on scattering amplitudes

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scattering Amplitudes and QFT Insight (Final Scientific Report)

The calculation of scattering amplitudes provides an invariant window into the physical dynamic content of relativistic quantum field theory. Yet with traditional methods, for empirically relevant theories, these calculations scale with a factorial complexity in external particles and precision. If we aspire to collapse the theoretical uncertainty obscuring new physics hidden at all scales from the microscopic probed at high energy colliders to the largest effective field theory in the universe governing the evolution of large scale structure, this complexity challenge necessitates new ideas and methods in calculation. Novel approaches like the color-kinematics duality and the associated double-copy construction have drastically simplified the situation, relating both gauge and gravity theory predictions to a much smaller kernel of invariant kinematic data. This project supporting research by the PI's Amplitudes and Insights group at Northwestern University looked to push insight deep into both the IR and the UV by establishing how novel structures must constrain the predictions of counterterms in both gauge and gravity theories, setting the groundwork to exploring the high energy behavior of particular gravity theories via constituent gauge-theory calculations, and confronting fundamental challenges at the interface between QFT amplitudes analysis and next generation gravitational wave science as well as well as inflationary and large scale structure cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗