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At least 217 records · Page 12

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NASA NTRS1988

A scattering model for forested area

A forested area is modeled as a volume of randomly oriented and distributed disc-shaped, or needle-shaped leaves shading a distribution of branches modeled as randomly oriented finite-length, dielectric cylinders above an irregular soil surface. Since the radii of branches have a wide range of sizes, the model only requires the length of a branch to be large compared with its radius which may be any size relative to the incident wavelength. In addition, the model also assumes the thickness of a disc-shaped leaf or the radius of a needle-shaped leaf is much smaller than the electromagnetic wavelength. The scattering phase matrices for disc, needle, and cylinder are developed in terms of the scattering amplitudes of the corresponding fields which are computed by the forward scattering theorem. These quantities along with the Kirchoff scattering model for a randomly rough surface are used in the standard radiative transfer formulation to compute the backscattering coefficient. Numerical illustrations for the backscattering coefficient are given as a function of the shading factor, incidence angle, leaf orientation distribution, branch orientation distribution, and the number density of leaves. Also illustrated are the properties of the extinction coefficient as a function of leaf and branch orientation distributions. Comparisons are made with measured backscattering coefficients from forested areas reported in the literature.

Karam, M. A.↗

DOE OSTI2021

Determining the leading-order contact term in neutrinoless double β decay

We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe - e - amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n ( p 1 ) n ( p 2 ) W + ( k ) → $ p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) $ , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ( NN ) scattering in the 1 S 0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1 S 0 NN scattering lengths. While our analysis is performed in the $ \overline{\mathrm{MS}} $ scheme, we express our final result in terms of the scheme-independent renormalized amplitude $ {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) $ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for $ {\mathcal{A}}_{\nu } $ , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1987

Diffraction as tunneling

A new approximation to the short-wavelength scattering amplitude from an impenetrable sphere is presented. It is uniform in the scattering angle and it is more accurate than previously known approximations (including Fock's theory of diffraction) by up to several orders of magnitude. It remains valid in the transition to long-wavelength scattering. It leads to a new physical picture of diffraction, as tunneling through an inertial barrier.

Nussenzveig, H. M.↗

DOE OSTI2025

Hidden amplitude zeros from the double-copy map

Recently, Arkani-Hamed proposed the existence of zeros in scattering amplitudes in certain quantum field theories including the cubic adjoint scalar theory Tr ( ϕ 3 ) , the S U ( N ) nonlinear sigma model and Yang-Mills theory. These hidden zeros are special kinematic points where the amplitude vanishes and factorizes into a product of lower-point amplitudes, similar to factorization near poles. In this paper, we show a close connection between the existence of such zeros and the double-copy map. In fact, compatibility with the Bern-Carrasco-Johansson relations requires the presence of these zeros. We also show that these zeros extend via the Kawai-Lewellen-Tye relations to special Galileon amplitudes and their corrections, evincing that these hidden zeros are also present in permutation-invariant amplitudes. Published by the American Physical Society 2025

Bartsch, Christoph (ORCID:0000000174296682)↗

DOE OSTI2024

Coulomb Branch Amplitudes from a Deformed Amplituhedron Geometry

The amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us to propose a “deformed” amplituhedron. Focusing on the four-particle amplitude, we introduce two deformation parameters, which can be interpreted as particle masses. We provide evidence that the mass pattern corresponds to a specific choice of vacuum expectation values on the Coulomb branch. The deformed amplitude is infrared finite, making the answer well defined in four dimensions. Leveraging four-dimensional integration techniques based on differential equations, we compute the amplitude up to two loops. In the limit where the deformation parameters are taken to zero, we recover the known Bern-Dixon-Smirnov amplitude. In the limit where only one deformation parameter is taken to zero, we find a connection to the angle-dependent cusp anomalous dimension. Published by the American Physical Society 2024

Physics↗

DOE OSTI2024

A collinear perspective on the Regge limit

The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1988

Eikonal solutions to optical model coupled-channel equations

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.

Cucinotta, Francis A.↗

NASA NTRS1991

Target correlation effects on neutron-nucleus total, absorption, and abrasion cross sections

Second order optical model solutions to the elastic scattering amplitude were used to evaluate total, absorption, and abrasion cross sections for neutron nucleus scattering. Improved agreement with experimental data for total and absorption cross sections is found when compared with first order (coherent approximation) solutions, especially below several hundred MeV. At higher energies, the first and second order solutions are similar. There are also large differences in abrasion cross section calculations; these differences indicate a crucial role for cluster knockout in the abrasion step.

Cucinotta, Francis A.↗

DOE OSTI2024

Universal features of 2 → N scattering in QCD and gravity from shockwave collisions

A remarkable double-copy relation of Einstein gravity to QCD in Regge asymptotics is Γ μ ν = 1 2 C μ C ν − 1 2 N μ N ν , where Γ μ ν is the gravitational Lipatov vertex in the 2 → 3 graviton scattering amplitude, C μ its Yang-Mills counterpart, and N μ the QED bremsstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing the 2 → N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2D effective field theory framework describing trans-Planckian 2 → N graviton scattering. We construct a quantitative correspondence between a semiclassical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to R S , L , R S , H ≪ b , where R S , L , R S , H are the respective emergent Schwarzchild radii generated in shockwave collisions and b is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in the close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2 → N amplitudes that incorporates graviton Reggeization and coherent graviton multiple scattering. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Quantum Algorithm for High Energy Physics Simulations

Simulating quantum field theories is a flagship application of quantum computing. However, calculating experimentally relevant high energy scattering amplitudes entirely on a quantum computer is prohibitively difficult. It is well known that such high energy scattering processes can be factored into pieces that can be computed using well established perturbative techniques, and pieces which currently have to be simulated using classical Markov chain algorithms. These classical Markov chain simulation approaches work well to capture many of the salient features, but cannot capture all quantum effects. To exploit quantum resources in the most efficient way, we introduce a new paradigm for quantum algorithms in field theories. This approach uses quantum computers only for those parts of the problem which are not computable using existing techniques. In particular, we develop a polynomial time quantum final state shower that accurately models the effects of intermediate spin states similar to those present in high energy electroweak showers with a global evolution variable. The algorithm is explicitly demonstrated for a simplified quantum field theory on a quantum computer.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1976

Scattering by spheres with nonisotropic refractive indices

Experimental scattering results using a microwave analog technique are described. Artificially constructed axially symmetric spheres with a graphite-like fine-layered composite structure and anisotropic refractive indices were employed to aid high-precision measurements of forward scattering under stable conditions (temperature, physical dimensions, electronic conditions) and to facilitate studies of the extinction and polarization of light by graphite particles in interstellar space. A theoretical approximation utilizing Mie theory for spheres with suitable orientation-dependent refractive indices is applied to account for changes in the complex forward-scattering amplitudes and phase in response to target orientation. The methods are extended to the full range of scattering angles, from the forward direction continuously to about 165 deg and at 180 deg. Agreement between experiment and prediction is close when the symmetry axis is parallel to the polarization.

Wang, R. T.↗

NASA NTRS1999

S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series

We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.

Bessis, D.↗

DOE OSTI2021

Bootstrap and amplitudes: a hike in the landscape of quantum field theory

This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories. We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic quantum field theories. Here, the first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the CP 1 model with the Fubini-Study metric arising from re-summation of the n-point interaction terms derived from amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Momentum shift and on-shell recursion relation for electroweak theory

We study the all-line transverse (ALT) shift which we developed for on-shell recursion of amplitudes for particles of any mass. We discuss the validity of the shift for general theories of spin ≤1, and illustrate the connection between Ward identity and constructibility for massive spin-1 amplitude under the ALT shift. We apply the shift to the electroweak theory, and various four-point scattering amplitudes among electroweak gauge bosons and fermions are constructed. We show explicitly that the four-point gauge boson contact terms in massive electroweak theory automatically arise after recursive construction, independent of UV completion, and they automatically cancel the terms growing as (energy) 4 at high energy. We explore UV completion of the electroweak theory that cancels the remaining (energy) 2 terms and impose unitarity requirements to constrain additional couplings. The ALT shift framework allows consistent treatment in dealing with contact term ambiguities for renormalizable massive and massless theories, which we show can be useful in studying real-world amplitudes with massive spinors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2000

Exchange Forces in Dispersion Relations Investigated Using Circuit Relations

We propose a novel method to compute in an exact manner the left-hand cut discontinuity of the electron-Atom partial wave scattering amplitude in the complex energy plane within the static stage approximation. Zero energy dispersion relations for electron-Hydrogen scattering are computed numerically for illustration.

Vrinceanu, D.↗

NASA NTRS1993

Influence of drift flow turbulence on surface gravity wave propagation

The theory of surface gravity waves scattering at vortex flows in the ocean is developed in this paper. A scattering amplitude is found in the Born approximation as a function of Vorticity that appears very convenient for investigation of scattering at simple localized flows.

drift flow turbulence↗

DOE OSTI2020

First-principles calculation of spin and orbital contributions to magnetically ordered moments in Sr 2 IrO 4

Here, we show how an accurate first-principles treatment of the canted-anti-ferromagnetic ground state of Sr 2 IrO 4 , a prototypical 5d correlated spin-orbit coupled material, can be obtained without invoking any free parameters, such as the Hubbard $\textit{U}$ or tuning the spin-orbit coupling strength. Our theoretically predicted iridium magnetic moment of 0.250$μ_B$, canted by 12.6° off the $\textit{a}$ axis, is in accord with experimental results. By resolving the magnetic moments into their spin and orbital components, we show that our theoretically obtained variation of the magnetic scattering amplitude $\langle M_m \rangle$ as a function of the polarization angle is consistent with recent nonresonant magnetic x-ray scattering measurements. The computed value of the band gap (55 meV) is also in line with the corresponding experimental values. A comparison of the band structure to that of the cuprates suggests the presence of incommensurate charge-density wave phases in Sr 2 IrO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Multi-hadron systems via Lattice QCD

This project supported a broad set of research in theoretical nuclear physics which has been designed to support current and future experimental DOE facilities. The broad summary of physical observables of interest in this project were the bread-and-butter observables obtained in experimental nuclear and particle physics experiments, namely scattering amplitude including multi-hadronic states. The primary goal of this project was to design a systematically improvable paradigm for accessing such amplitudes directly from the Standard Model of Particle Physics. The main tools that were used and explored in this project were scattering theory, lattice QCD, and future quantum computers. The physics outputs included various novel formalisms, exploratory lattice QCD calculations, and a new proposal for studying any scattering observable using future quantum computers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗