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All sources NASA NTRS DOE OSTI

DOE OSTI2016

Hadron scattering and resonances in QCD

I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study pi pi elastic scattering, including the rho resonance, as well as coupled-channel pi K, eta K scattering. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.

Dudek, Jozef J.↗

NASA NTRS1993

Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

A microscopic model for the quasiparticle interaction in neutron matter is presented. Both-particle (pp) and particle-hole (ph) correlations are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for particle-hole interaction and the scattering amplitude of the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules for the scattering amplitude are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the (1)S(sub 0) gap parameter for neutron superfluidity and comment briefly on neutron-star implications.

Wambach, J↗

DOE OSTI2025

Tropical amplitudes for colored Lagrangians

Recently a new formulation for scattering amplitudes in Tr(Φ 3 ) theory has been given based on simple combinatorial ideas in the space of kinematic data. This allows all-loop integrated amplitudes to be expressed as “curve integrals” defined using tropical building blocks — the “headlight functions”. This paper shows how the formulation extends to the amplitudes of more general Lagrangians. We will present a number of different ways of introducing tropical “numerator functions” that allow us to describe general Lagrangian interactions. The simplest family of these “tropical numerators” computes the amplitudes of interesting Lagrangians with infinitely many interactions. We also describe methods for tropically formulating the amplitudes for general Lagrangians. One uses a variant of “Wick contraction” to glue together numerator factors for general interaction vertices. Another uses a natural characterization of polygons on surfaces to give a novel combinatorial description of all possible diagrams associated with arbitrary valence interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Quark-Mass Dependence of Elastic $πK$ Scattering from QCD

We present a determination of the isospin-½ elastic $πK$ scattering amplitudes in $S$ and $P$ partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the $P$-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $κ/K_{0}^{*}$(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Positive Parity $D_s$ Mesons

We study the positive parity charmed strange mesons using lattice QCD, the only reliable ab initio method to study QCD at low energies. Especially the experimentally observed $D_{s0}^*(2317)$ and $D_{s1}(2460)$ have challenged theory for quite some time. The dynamical lattice QCD simulations are performed at two distinct pion masses, $m_{\pi}$ = 266 MeV and 156 MeV, using both $\bar{c}s$ as well as $DK$ and $D^*K$ scattering operators in the construction of the correlation matrix in order to take into the account threshold effects. While the $J^P = 0^+$ channel benefited most from the inclusion of scattering operators, it was also crucial for the case of the $D_{s1}(2460)$. Using the L\"uscher method, which relates the finite volume spectrum to the infinite volume scattering matrix, we were able to determine the near threshold behavior of the scattering amplitude. From it we extracted the binding momenta and the masses of the below-threshold bound states $D_{s0}^*(2317)$ and $D_{s1}(2460)$ by determining the pole positions of the scattering amplitudes. Our results compare well with experiment, resolving a long standing discrepancy between theory and experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes’ theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. In conclusion, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1982

High Frequency Scattering from Arbitrarily Oriented Dielectric Disks

Calculations have been made of electromagnetic wave scattering from dielectric disks of arbitrary shape and orientation in the high frequency (physical optics) regime. The solution is obtained by approximating the fields inside the disk with the fields induced inside an identically oriented slab (i.e. infinite parallel planes) with the same thickness and dielectric properties. The fields inside the disk excite conduction and polarization currents which are used to calculate the scattered fields by integrating the radiation from these sources over the volume of the disk. This computation has been executed for observers in the far field of the disk in the case of disks with arbitrary orientation and for arbitrary polarization of the incident radiation. The results have been expressed in the form of a dyadic scattering amplitude for the disk. The results apply to disks whose diameter is large compared to wavelength and whose thickness is small compared to diameter, but the thickness need not be small compared to wavelength. Examples of the dependence of the scattering amplitude on frequency, dielectric properties of the disk and disk orientation are presented for disks of circular cross section.

Levine, D. M.↗

DOE OSTI2022

Nonperturbative negative geometries: amplitudes at strong coupling and the amplituhedron

The amplituhedron determines scattering amplitudes in planar N = 4 super Yang-Mills by a single “positive geometry” in the space of kinematic and loop variables. We study a closely related definition of the amplituhedron for the simplest case of four-particle scattering, given as a sum over complementary “negative geometries”, which provides a natural geometric understanding of the exponentiation of infrared (IR) divergences, as well as a new geometric definition of an IR finite observable F(g, z) — dually interpreted as the expectation value of the null polygonal Wilson loop with a single Lagrangian insertion — which is directly determined by these negative geometries. This provides a long-sought direct link between canonical forms for positive (negative) geometries, and a completely IR finite post-loop-integration observable depending on a single kinematical variable z, from which the cusp anomalous dimension Γ cusp (g) can also be straightforwardly obtained. We study an especially simple class of negative geometries at all loop orders, associated with a “tree” structure in the negativity conditions, for which the contributions to F(g, z) and Γ cusp can easily be determined by an interesting non-linear differential equation immediately following from the combinatorics of negative geometries. This lets us compute these “tree” contributions to F(g, z) and Γ cusp for all values of the ‘t Hooft coupling. The result for Γ cusp remarkably shares all main qualitative characteristics of the known exact results obtained using integrability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Chiral symmetry and π - π scattering in the Covariant Spectator Theory

The π-π scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similarly to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward Takahashi identity to the CST π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. Thus, the Adler self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Scalar and Tensor Charmonium Resonances in Coupled-Channel Scattering from Lattice QCD

We determine J P C = 0 + + and 2 + + hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at m π ≈ 391 MeV , more than 200 finite-volume energy levels are computed and these are used in extensions of the Lüscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single χ c 0 and a single χ c 2 resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically closed D * D ¯ * channels in S -wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state χ c 0 , no other scalar bound states or near- D D ¯ threshold resonances are found, in contrast to several theoretical and experimental studies. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

SFDBSI_GLS v. 1.0

Matlab code for inversion of frequency domain, electrostatic geophysical data in terms of scalar scattering amplitudes in the subsurface. The data is assumed to be the difference between two measurements: electric field measurements prior to the injection of an electrically conductive proppant, and the electric field measurements after proppant injection. The proppant is injected into the subsurface via a well, and its purpose is to prop open fractures created by hydraulic fracturing. In both cases the illuminating electric field is assumed to be a vertically incident plane wave. The inversion strategy is to solve a set of linear system of equations, where each equation defines the amplitude of a candidate scattering volume. The model space is defined by M potential scattering locations and the frequency domain (of which there are k frequencies) data are recorded on N receivers. The solution thus solves a kN x M system of linear equations for M scalar amplitudes within the user-defined solution space. Practical Application: Oilfield environments where observed electrostatic geophysical data can reasonably be assumed to be scattered by subsurface proppant volumes. No field validation examples have so far been provided.

Poppeliers, Christian↗

DOE OSTI2025

Processing-dependent chemical ordering in Cu 3 Au characterized via non-destructive Bragg coherent diffraction imaging

Of current importance for alloy design is controlling chemical ordering through processing routes to optimize an alloy's mechanical properties for a desired application. However, characterization of chemical ordering remains an ongoing challenge, particularly when nondestructive characterization is needed. Here, in this study, Bragg coherent diffraction imaging is used to reconstruct morphology and lattice displacement in model Cu 3 Au nanocrystals that have undergone different heat treatments to produce variation in chemical ordering. The magnitudes and distributions of the scattering amplitudes (proportional to electron density) and lattice strains within these crystals are then analyzed to correlate them to the expected amount of chemical ordering present. Nanocrystals with increased amounts of ordering are found to generally have less extreme strains present and reduced strain distribution widths. In addition, statistical correlations are found between the spatial arrangement of scattering amplitude and lattice strains.

Warren, Nathaniel [Pennsylvania State Univ., Unive↗

DOE OSTI2024

Pion Nucleon Scattering in BCHPT Combined with 1/Nc Expansion

Pion nucleon scattering has played a crucial role in advancing our understanding of the low-energy regime of strong interactions. This dissertation presents the development of a new theoretical framework that combines Baryon Chiral Perturbation Theory (BChPT) with the 1/Nc Expansion to analyze pion nucleon scattering. The resulting effective Lagrangian incorporates both chiral and spin-flavor symmetries. Scattering amplitudes are calculated up to the one-loop level (NNLO), which includes four tree-level Feynman diagrams and 45 non-zero loop diagrams. The effective Lagrangian is renormalized at the one-loop level. With spin-3/2 baryons naturally included, the framework demonstrates strong convergence at higher energies. The NNLO pion nucleon scattering amplitude shows good agreement with experimental data from the SAID database. This novel approach, BChPT combined with 1/Nc Expansion, demonstrates substantial predictive power at higher energies where other low-energy theories fall short, achieving the goals of this combined framework. The contribution from loop diagrams is essential for achieving good agreement with the data, highlighting the importance of conducting the calculation up to NNLO. Extracted values for physically measurable quantities agree reasonably well with independently extracted values, underscoring the robustness of the theory.

Jayakodige, Dulitha [Hampton Univ., Hampton, VA (U↗

DOE OSTI2024

Two-Pole Nature of the Λ ( 1405 ) Resonance from Lattice QCD

This Letter presents the first lattice QCD computation of the coupled channel π Σ − K ¯ N scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance Λ ( 1405 ) with strangeness S = − 1 and isospin, spin, and parity quantum numbers I ( J P ) = 0 ( 1 / 2 − ) . However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to m π ≈ 200 MeV and m K ≈ 487 MeV , this study finds the amplitudes exhibit a virtual bound state below the π Σ threshold in addition to the established resonance pole just below the K ¯ N threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Lattice QCD study of π Σ − K ¯ N scattering and the Λ ( 1405 ) resonance

A lattice QCD computation of the coupled channel π Σ – K ¯ N scattering amplitudes in the Λ ( 1405 ) region is detailed. Results are obtained using a single ensemble of gauge field configurations with N f = 2 + 1 dynamical quark flavors and m π ≈ 200 MeV and m K ≈ 487 MeV . Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering K -matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the π Σ threshold and a resonance pole just below the K ¯ N threshold. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Resonances in Coupled-Channel Scattering of Light Mesons from Lattice QCD

Recent calculations of light meson scattering will be presented. Several advances have made it possible to extract coupled-channel hadron-hadron scattering amplitudes in a systematically improvable way using lattice QCD. The methods used in some of these first calculations will be explained in detail, and specific applications will be described. I will focus on channels involving pairs of ?, K, ?,?? mesons. Finite volume energy levels describing these systems are obtained from large correlation matrices that are then diagonalized using the variational method to obtain a spectrum. These finite volume spectra are then used to constrain infinite volume scattering amplitudes that may in turn be analyzed for their pole content to extract resonance properties.

Wilson, David↗

DOE OSTI2023

Double-copy towards supergravity inflation with α-attractor models

A bstract Key to the simplicity of supergravity α -attractor models of inflation are Volkov-Akulov fermions, often in the form of nilpotent superfields. Here we explore the possibility of using the double-copy to construct theories of Dirac-Born-Infeld-Volkov-Akulov (DBIVA) coupled to supergravity. A color-dual bootstrap admits scattering amplitudes involving pions and vectors through five-point tree-level order by order in mass-dimension, but requires the introduction of a Tr( F 3 ) operator. Gauge theories with this operator were recently found to require a tower of higher-derivative operators to be compatible with the duality between color and kinematics. Adjoint-type double-copy construction at its most conservative seems to require the UV completion of DBIVA + pure Poincaré supergravity scattering amplitudes to a family of theories involving DBIVA-like particles coupled to Weyl-Einstein supergravity. We also point out an alternative solution to color-dual gauged pions that allows adjoint double-copy without a tower of higher derivative corrections but at the cost of exchange symmetry between scalars.

Physics↗

DOE OSTI2021

Quantum field theory and the Bieberbach conjecture

An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and the non-perturbative crossing symmetric representation of 2-2 scattering amplitudes of identical scalars is pointed out. Using the dispersion relation and unitarity, we are able to derive several inequalities, analogous to those which arise in the discussions of the Bieberbach conjecture. We derive new and strong bounds on the ratio of certain Wilson coefficients and demonstrate that these are obeyed in one-loop Φ 4 theory, tree level string theory as well as in the S-matrix bootstrap. Further, we find two sided bounds on the magnitude of the scattering amplitude, which are shown to be respected in all the contexts mentioned above. Translated to the usual Mandelstam variables, for large |s|, fixed t, the upper bound reads |M(s,t)| ≲ |s 2 |. We discuss how Szegö's theorem corresponds to a check of univalence in an EFT expansion, while how the Grunsky inequalities translate into nontrivial, nonlinear inequalities on the Wilson coefficients.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗