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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Partial-wave projection of relativistic three-body amplitudes

We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy 𝑆 matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, 𝒦 3 , in two equivalent formalisms—one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parametrizations useful for amplitude analysis. Finally, we examine toy models for 3⁢𝜋 systems at unphysically heavy pion masses with total isospins 0, 1, and 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Spinning black hole scattering at $ \mathcal{O} $(G 3 S 2 )(G 3 S 2 ): Casimir terms, radial action and hidden symmetry

We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to S 2 = −s(s+1)ħ 2 , using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at $ \mathcal{O} $(G 3 S 2 ), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a root-Kerr electromagnetic background up to $ \mathcal{O} $(α 3 S 2 ). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.

Classical Theories of Gravity↗
NASA NTRS2007

Application of the Finite Element Method in Atomic and Molecular Physics

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Shertzer, Janine↗
DOE OSTI2025

Scalar-scaffolded gluons and the combinatorial origins of Yang-Mills theory

We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr Φ 3 theory. We propose that in a precise sense the amplitudes for a suitably “stringy” form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for n gluons via a “scalar scaffolding”, arising from the scattering of 2n colored scalars coming in n distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the “u-variables”, describing the “binary geometry” for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr Φ 3 amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop-level gluon cuts. Our “stringy” scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the u variables autonomously “knows” about everything needed to convert colored scalar to gluon amplitudes, exposing a striking “discovery” of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1993

Scattering calculations and confining interactions

Most of the research work performed under this grant were concerned with strong interaction processes ranging from kaon-nucleon interaction to proton-nucleus scattering calculations. Research performed under this grant can be categorized into three groups: (1) parametrization of fundamental interactions, (2) development of formal theory, and (3) calculations based upon the first two. Parametrizations of certain fundamental interactions, such as kaon-nucleon interaction, for example, were necessary because kaon-nucleon scattering amplitude was needed to perform kaon-nucleus scattering calculations. It was possible to calculate kaon-nucleon amplitudes from the first principle, but it was unnecessary for the purpose of the project. Similar work was also done for example for anti-protons and anti-nuclei. Formal developments to some extent were also pursued so that consistent calculations can be done.

Buck, Warren W.↗
DOE OSTI2025

All loop scattering as a counting problem

Abstract This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ’t Hooft expansion. We find novel integral formulas for the amplitudes of this theory, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

1/N Expansion↗
DOE OSTI2025

Cosmohedra

It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr(ϕ 3 ) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note, we describe a new class of polytopes — “cosmohedra” — that provide a natural solution to this problem. The faces of associahedra capture the combinatorics of non-overlapping chords of the momentum polygon, reflecting all partial factorizations of amplitudes. Cosmohedra are far richer — instead of non-overlapping chords, their faces capture the “russian doll” structure of non-overlapping subpolygons that determine the wavefunction. We show that cosmohedra are intimately related to associahedra, obtained by “blowing up” faces of the associahedron in a simple way. We give a full combinatorial description of cosmohedron faces and their factorization properties, and provide an explicit realization in terms of facet inequalities that further “shave” the facet inequalities of the associahedron. We also discuss a novel way for computing the wavefunction from cosmohedron geometry that extends the usual connection with polytope canonical forms. We illustrate cosmohedra with examples at tree-level and one loop; the close connection to surfacehedra suggests the generalization to all loop orders. Moving beyond the wavefunction, we briefly describe “cosmological correlahedra” for full correlators, which are one higher-dimensional polytopes, interpolating between associahedra and cosmohedra on opposite facets in an extra direction associated with the total energy. We speculate on how the existence of cosmohedra might suggest a “stringy” formulation for the cosmological wavefunction/correlators, generalizing the way in which the Minkowski sum decomposition of associahedra naturally extend particle to string amplitudes.

Scattering Amplitudes↗
DOE OSTI2026

Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins

We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, I πππ = 2, 1 and 0. Using the generic-isospin extension of the RFT formalism [1] and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum P in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.

hadronic spectroscopy↗
DOE OSTI2025

All loop scattering for all multiplicity

We study the recently introduced curve integral formalism that defines a new family of formulas for the scattering amplitudes of the colored scalar trϕ 3 theory. We find that the curve integral manifests a very surprising fact about these amplitudes: the dependence on the number of particles, n, and the loop order, L, is effectively decoupled in these formulas. We derive the curve integrals at tree-level for all n. We then show that, for higher loop-order, it suffices to study the curve integrals for L-loop tadpole-like amplitudes, which have just one particle per color trace-factor. By combining these tadpole-like formulas with the tree-level results, we find formulas for the all n amplitudes at L loops. We illustrate this result by giving explicit curve integrals for all the amplitudes in the theory, including the non-planar amplitudes, through to two loops, for all n.

1/N Expansion↗
DOE OSTI2025

From Feynman diagrams to the amplituhedron: a gentle review

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.

Feynman diagrams↗
DOE OSTI2025

Gravitational memory and Ward identities in the local detector frame

Gravitational memory, which describes the permanent shift in the strain after the passage of gravitational waves, is directly related to Weinberg’s soft graviton theorems and the Bondi-Metzner-Sachs (BMS) symmetry group of asymptotically flat space-times. In this work, we provide an equivalent description of the phenomenon in local coordinates around gravitational wave detectors, such as transverse-traceless (TT) gauge. We show that gravitational memory is encoded in large residual diffeomorphisms in this gauge, which include time-dependent anisotropic spatial rescalings, and prove their equivalence to BMS transformations when translated to TT gauge. We then derive the associated Ward identities and associated soft theorems, for both scattering amplitudes and equal-time (in-in) correlation functions, and explicitly check their validity for planar gravitational waves. Furthermore, the in-in identities are recognized as the flat-space analog of the well-known inflationary consistency relations.

General relativity↗
DOE OSTI2025

Gravitational memory and soft theorems: The local perspective

In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. Furthermore, these relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators.

General relativity↗
DOE OSTI2026

Dispersive and nondispersive 𝐾-matrix formalisms

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The 𝐾-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive 𝐾-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under 𝐾-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Geometry of soft scalars at one loop

We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating IR-divergent loop integrals; new results for the soft limit of general scalar one-loop integrals are presented. The geometric soft theorem remains unmodified for any derivatively-coupled scalar effective field theory, and we conjecture that this statement holds to all orders. In contrast, the soft theorem receives nontrivial corrections in the presence of potential interactions, analogous to the case of non-Abelian gauge theories. We derive the universal leading-order correction to the scalar soft theorem arising from potential interactions at one loop. Explicit examples are provided that illustrate the general results.

differential and algebraic geometry↗
DOE OSTI2025

BCFW tilings and cluster adjacency for the amplituhedron

In 2005, Britto, Cachazo, Feng, and Witten gave a recurrence (now known as the BCFW recurrence) for computing scattering amplitudes in N = 4 super Yang–Mills theory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to give a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka conjectured that each way of iterating the BCFW recurrence gives a “triangulation” or “tiling” of the m=4 amplituhedron. In this article, we prove the BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster adjacency conjecture for BCFW tiles of the amplituhedron, which says that facets of tiles are cut out by collections of compatible cluster variables for the Grassmannian Gr4,n. Moreover we show that each BCFW tile is the subset of the Grassmannian where certain cluster variables have particular signs.

97 MATHEMATICS AND COMPUTING↗