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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

The scattering of spinning hadrons from lattice QCD

Hadron spectroscopy is predominantly the study of resonances that decay via the strong interaction into a multitude of stable hadrons, such as the pion. The vast majority of resonances decay via an intermediate hadron with non-zero intrinsic spin. In this thesis, I will present the results of scattering calculations featuring mesons with non-zero intrinsic spin. Before doing so, I will first give a brief introduction to QCD and review the framework necessary to perform lattice QCD calculations in Chapters 1 and 2. In Chapter 3, I present the first lattice calculation of ?? scattering in isospin-2. Here, ?? features in dynamically-coupled 3S1 and 3D1 partial-waves with JP=1+. No resonance enhancement is anticipated in the flavour exotic isospin-2 channel and as such it provides an ideal testing ground for this first calculation. I work at heavier than physical quark masses at the SU(3)F point where the up, down and strange quarks are mass degenerate. Finite-volume spectra are calculated and, utilising the relationship between the discrete energy spectrum and the infinite-volume scattering amplitudes, partial-wave amplitudes with J?3 and the degree of dynamical mixing between the coupled 3S1 and 3D1 channels are determined. In Chapter 4, I investigate ?? in isospin-1 where the a1 axial-vector resonance is expected to feature. Here, I present a discussion on G-parity and Bose-symmetry at the SU(3)F point. Working at heavier than physical quark masses, the resulting finite volume spectrum suggests that the a1 is a bound-state and that the 3S1- and 3D1-wave, ?? scattering amplitudes are similar to those in isospin-2. I present the first calculation of coupled ?? and ?? scattering in Chapter 5 where resonant enhancement is seen experimentally in the JP=1+ channel. Working at a somewhat lighter pion mass than in previous chapters, the finite-volume spectra are determined and the scattering amplitudes are calculated. Analytically continuing the amplitudes into the complex energy plane, a resonance pole is found, interpreted as the analogue of the b1 axial-vector, which couples dominantly to 3S1-wave ??, with a much-suppressed coupling to 3D1-wave ??, and a negligible coupling to ??. In Chapter 6, the exotic JPC=1?+ channel is studied. These quantum numbers are not allowed in the quark model but can be obtained, for example, through a gluonic excitation coupled to a quark-antiquark pair. In this exploratory calculation, performed at the SU(3)F point, the finite-volume spectra and coupled-channel scattering amplitudes are presented. A single resonance pole is found, interpreted as the exotic ?1, and couplings to meson-meson channels, including for example ??{1P1}, ???{1P1} and ??{3P1}, are calculated for the first time in lattice QCD. In order to minimally present the contents of a unitary n-channel scattering matrix, I introduce, in Chapter 7, an n-channel generalisation of the traditional two-channel Stapp parameterisation.

Woss, Antoni↗
NASA NTRS1979

Multiple scattering and charged-particle - hydrogen-atom collisions

Glauber-approximation scattering amplitudes for charged-particle - hydrogen-atom elastic and inelastic collisions are derived directly in terms of the known particle-electron and particle-proton Coulomb scattering amplitudes and the known hydrogen-atom form factors. It is shown that the particle-hydrogen amplitude contains no single-scattering term. The double-scattering term is obtained as a two-dimensional integral in momentum space. It is demonstrated how the result can be used as the starting point for an alternative and relatively simple derivation, in closed form, of the Glauber particle-hydrogen scattering amplitude for transitions from the ground state to an arbitrary (nlm) state.

Franco, V.↗
DOE OSTI2016

Positive signs in massive gravity

Here, we derive new constraints on massive gravity from unitarity and analyticity of scattering amplitudes. Our results apply to a general effective theory defined by Einstein gravity plus the leading soft diffeomorphism-breaking corrections. We calculate scattering amplitudes for all combinations of tensor, vector, and scalar polarizations. Furthermore, the high-energy behavior of these amplitudes prescribes a specific choice of couplings that ameliorates the ultraviolet cutoff, in agreement with existing literature. We then derive consistency conditions from analytic dispersion relations, which dictate positivity of certain combinations of parameters appearing in the forward scattering amplitudes. These constraints exclude all but a small island in the parameter space of ghost-free massive gravity. And while the theory of the "Galileon" scalar mode alone is known to be inconsistent with positivity constraints, this is remedied in the full massive gravity theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders

We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansätze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts — expressed as products of tree amplitudes — to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes.

Effective Field Theories↗
DOE OSTI2024

Two-loop master integrals for leading-color $$ pp\to t\overline{t}H $$ amplitudes with a light-quark loop

Abstract We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in$$ t\overline{t}H $$ t t ¯ H production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a basis of master integrals satisfying a system of differential equations inϵ-factorized form. We present the analytic form of the differential equations in terms of a minimal set of differential one-forms. We explore properties of the function space of analytic solutions to the differential equations in terms of iterative integrals which can be exploited for studying the analytic form of related scattering amplitudes. Finally, we solve the differential equations using generalized series expansions to numerically evaluate the master integrals in physical phase space. As the first computation of a set of two-loop seven-scale master integrals, our results provide valuable input for analytic studies of scattering amplitudes in processes involving massive particles and a large number of kinematic scales.

Physics↗
DOE OSTI2014

The Amplituhedron

Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for \( \mathcal{N}=4 \) SYM scattering amplitudes in the planar limit, which we identify as “the volume” of a new mathematical object — the Amplituhedron — generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

From QCD to physical resonances

Here in this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at m π = 236 MeV [1], for the isotriplet ππ channel are analyzed using the Lüscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to the complex plane to obtain the ρ -pole at [ 755 ( 2 ) ( 1 ) ( 02 20 ) - i 2 129 ( 3 ) ( 1 ) ( 1 7 ) ]

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Polarization Transfer in Wide-Angle Compton Scattering and Single-Pion Photoproduction from the Proton

Wide-angle exclusive Compton scattering and single-pion photoproduction from the proton have been investigated via measurement of the polarization transfer from a circularly polarized photon beam to the recoil proton. The wide-angle Compton scattering polarization transfer was analyzed at an incident photon energy of 3.7 GeV at a proton scattering angle of theta(p)(cm) cm = 70 degrees. The longitudinal transfer K-LL, measured to be 0.645 +/- 0.059 +/- 0.048, where the first error is statistical and the second is systematic, has the same sign as predicted for the reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton. However, the observed value is similar to 3 times larger than predicted by the generalized-parton-distribution-based calculations, which indicates a significant unknown contribution to the scattering amplitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1979

Theory of direct scattering of neutral and charged atoms

The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.

Franco, V.↗
DOE OSTI2022

Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

All orders results for self-crossing Wilson loops mimicking double parton scattering

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar N = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. Furthermore, we also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

1/N expansion scattering amplitudes↗
DOE OSTI2025

Near-threshold states in coupled D D * − D * D * scattering from lattice QCD

The first determination of doubly charmed isospin-0 coupled-channel D D * − D * D * scattering amplitudes from lattice quantum chromodynamics (QCD) is presented. The finite-volume spectrum is computed for three lattice volumes with a light-quark mass corresponding to m π ≈ 391 MeV and is used to extract the scattering amplitudes in J P = 1 + via the Lüscher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a T c c pole corresponding to a virtual bound state is found below D D * threshold. We also find a second pole, T c c ′ , corresponding to a resonance pole below the kinematically closed D * D * channel, to which it has a strong coupling. A nonzero coupling is robustly found between the S -wave D D * and D * D * channels producing a clear cusp in the D D * amplitude at the D * D * threshold energy. This suggests that the experimental T c c ′ should be observable in D D * and D * D * final states at ongoing experiments. Published by the American Physical Society 2025

Whyte, Travis (ORCID:000000027661301X)↗
NASA NTRS1993

LRAT: Lightning Radiative Transfer

In this report, we extend to cloud physics the work done for single and multiple scattering of electromagnetic waves. We consider the scattering of light, visible or infrared, by a spherical cloud represented by a statistically homogeneous ensemble of configurations of N identical spherical water droplets whose centers are uniformly distributed in its volume V. The ensemble is specified by the average number rho of scatterers in unit volume and by rho f(R) with f(R) as the distribution function for separations R of pairs. The incident light, vector-phi(sub 0) a plane electromagnetic wave with harmonic time dependence, is from outside the cloud. The propagation parameter kappa(sub 0) and the index of refraction eta(sub 0) determine physically the medium outside the distribution of scatterers. We solve the interior problem separately to obtain the bulk parameters for the scatterer equivalent to the ensemble of spherical droplets. With the interior solution or the equivalent medium approach, the multiple scattering problem is reduced to that of an equivalent single scatterer excited from outside illumination. A dispersion relation which determines the bulk propagation parameter K and the bulk index of refraction eta of the cloud is given in terms of the vector equivalent scattering amplitude vector-G and the dyadic scattering amplitude tilde-g of the single object in isolation. Based on this transfer model we will have the ability to consider clouds composed of inhomogeneous distribution of water and/or ice particles and we will be able to take into account particle size distributions within the cloud. We will also be able to study the effects of cloud composition (i.e., particle shape, size, composition, orientation, location) on the polarization of the single or the multiple scattered waves. Finally, this study will provide a new starting point for studying the problem of lightning radiative transfer.

Phanord, Dieudonne D.↗
DOE OSTI2020

The cosmological bootstrap: inflationary correlators from symmetries and singularities

Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and the particle content of the theory. For example, four-particle amplitudes are analytic for contact interactions and have simple poles with appropriately positive residues for tree-level exchange. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlation functions are controlled by an approximate conformal symmetry on the boundary of the spacetime. After systematically classifying all possible contact terms in de Sitter space, we derive an analytic expression for the four-point function of conformally coupled scalars mediated by the tree-level exchange of massive scalars. Conformal symmetry implies that the correlator satisfies a pair of differential equations with respect to spatial momenta, encoding bulk time evolution in purely boundary terms. The absence of unphysical singularities (and the correct normalization of physical ones) completely fixes this correlator. Moreover, a “spin-raising” operator relates it to the correlators associated with the exchange of particles with spin, while “weight-shifting” operators map it to the four-point function of massless scalars. We explain how these de Sitter four-point functions can be perturbed to obtain inflationary three-point functions. Using our formalism, we reproduce many classic results in the literature, such as the three-point function of slow-roll inflation, and provide a complete classification of all inflationary three- and four-point functions arising from weakly broken conformal symmetry. Remarkably, the inflationary bispectrum associated with the exchange of particles with arbitrary spin is completely characterized by the soft limit of the simplest scalar-exchange four-point function of conformally coupled scalars and a series of contact terms. Finally, we demonstrate that the inflationary correlators contain flat-space scattering amplitudes via a suitable analytic continuation of the external momenta, which can also be directly connected with the signals for particle production seen in the squeezed limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Light and Strange Vector Resonances from Lattice QCD at Physical Quark Masses

We present the first ab initio calculation at physical quark masses of scattering amplitudes describing the lightest pseudoscalar mesons interacting via the strong force in the vector channel. Using lattice quantum chromodynamics, we postdict the defining parameters for two short-lived resonances, the ρ(770) and K*(892) which manifest as complex energy poles in ππ and Kπ scattering amplitudes, respectively. The calculation proceeds by first computing the finite-volume energy spectrum of the two-hadron systems and then determining the amplitudes from the energies using the Lüscher formalism. The error budget includes a data-driven systematic error, obtained by scanning possible fit ranges and fit models to extract the spectrum from Euclidean correlators, as well as the scattering amplitudes from the latter. The final results, obtained by analytically continuing multiple parametrizations into the complex energy plane, are M ρ = 796(5)(50)MeV, Γ ρ = 192(10)(31) MeV, M K* = 893(2)(54) MeV, and Γ K = 51(2)(11) MeV, where the subscript indicates the resonance and M and Γ stand for the mass and width, respectively, and where the first bracket indicates the statistical and the second bracket the systematic uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Absorptive effects and classical black hole scattering

Abstract We describe an approach to incorporating the physical effects of the absorption of energy by the event horizon of black holes in the scattering amplitudes based post-Minkowskian, point-particle effective description. Absorptive dynamics are incorporated in a model-independent way by coupling the usual point-particle description to an invisible sector of gapless internal degrees-of-freedom. The leading order dynamics of this sector are encoded in the low-energy expansion of a spectral density function obtained by matching an absorption cross section in the ultraviolet description. This information is then recycled using the scattering amplitudes based Kosower-Maybee-O’Connell in-in formalism to calculate the leading absorptive contribution to the impulse and change in rest mass of a Schwarzschild black hole scattering with a second compact body sourcing a massless scalar, electromagnetic or gravitational field. The results obtained are in complete agreement with previous worldline Schwinger-Keldysh calculations and provide an alternative on-shell scattering amplitudes approach to incorporating horizon absorption effects in the gravitational two-body problem.

Physics↗
DOE OSTI2021

BCJ amplitude relations for Anti-de Sitter boundary correlators in embedding space

We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the Nonlinear Sigma Model through four- and six-points, respectively. For the latter we also find representations of the four- and six-point correlator that manifest the duality. Possible double-copy procedures in AdS space are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the D-dimensional decomposition of integrands of scattering amplitudes into master and surface terms, the computation of tree-level amplitudes in floating point or finite-field arithmetic, the numerical computation of one- and two-loop amplitudes in QCD and Einstein gravity, and functional reconstruction tools. Here, we provide programs that showcase Caravel's main functionalities and allow to compute selected one- and two-loop amplitudes.

97 MATHEMATICS AND COMPUTING↗