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Related papers: Open associahedra and scattering forms

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Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\pi$, $K$ and $\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain…

High Energy Physics - Lattice · Physics 2016-11-23 David J. Wilson

Various methods for the recursive evaluation of scattering amplitudes in quantum field theory and string theory have been put forward during the last couple of years. In these proceedings we describe a geometrical framework, which is…

High Energy Physics - Theory · Physics 2021-07-09 Johannes Broedel , André Kaderli

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic…

Computational Geometry · Computer Science 2015-10-20 Joseph O'Rourke

In this work we present scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain. This model is directly derived from the two point correlation function with the inclusion of excluded volume…

Soft Condensed Matter · Physics 2014-07-25 Xin Li , Christopher N. Lam , Luis E. Sánchez-Diáz , Gregory S. Smith , Bradley D. Olsen , Wei-Ren Chen

One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

Geometric Topology · Mathematics 2013-11-13 Frank Quinn

It is proven here that the diameter of the d-dimensional associahedron is 2d-4 when d is greater than 9. Two maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon, and their distance is…

Combinatorics · Mathematics 2014-03-31 Lionel Pournin

We interpret cooperative scattering by a collection of cold atoms as a multiple scattering process. Starting from microscopic equations describing the response of $N$ atoms to a probe light beam, we represent the total scattered field as an…

Facets of the convex hull of $n$ independent random vectors chosen uniformly at random from the unit sphere in $\mathbb{R}^d$ are studied. A particular focus is given on the height of the facets as well as the expected number of facets as…

Probability · Mathematics 2019-08-13 Gilles Bonnet , Eliza O'Reilly

We study the interaction of two scattering channels for a simple geometric model consisting in a double covering of the plane with two branch points, equipped with the Euclidean metric. We show that the scattering channels are open in the…

Spectral Theory · Mathematics 2017-12-27 Rainer Hempel , Olaf Post

We explore how various topics in modern scattering amplitudes research find application in the description of collider physics processes. After a brief review of experimentally measured quantities and how they are related to amplitudes, we…

High Energy Physics - Theory · Physics 2023-01-10 Chris D. White

We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…

High Energy Physics - Theory · Physics 2015-12-22 Rijun Huang , Junjie Rao , Bo Feng , Yang-Hui He

Recently, "cosmohedra" have been introduced as polytopes underlying the cosmological wavefunction for conformally coupled Tr($\Phi^3$) theory in FRW cosmologies, generalizing associahedra for flat space scattering amplitudes. In this letter…

High Energy Physics - Theory · Physics 2026-01-08 Carolina Figueiredo , Francisco Vazão

We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…

Combinatorics · Mathematics 2012-11-02 Edward D. Kim

We describe a new sequence of polytopes which characterize A_infinity maps from a topological monoid to an A_infinity space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Later term(s) in our sequence…

Category Theory · Mathematics 2008-05-08 Stefan Forcey

The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for $\text{Tr}(\Phi^3)$ theory. Its faces were conjectured to be in bijection with Matryoshkas, which are obtained from a subdivision of a polygon…

Combinatorics · Mathematics 2026-03-23 Federico Ardila-Mantilla , Nima Arkani-Hamed , Carolina Figueiredo , Francisco Vazão

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time…

High Energy Physics - Theory · Physics 2008-11-26 Diana Vaman , York-Peng Yao

We investigate properties of four point colour ordered scattering amplitudes in D=6 fishnet CFT. We show that such amplitudes are related via very simple relation to their D=4 counterparts considered previously in the literature. Exploiting…

High Energy Physics - Theory · Physics 2021-05-18 L. V. Bork , R. M. Iakhibbaev , N. B. Muzhichkov , E. S. Sozinov

Scattering amplitudes have their origin in quantum field theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of…

High Energy Physics - Theory · Physics 2022-10-04 David A. Kosower , Ricardo Monteiro , Donal O'Connell

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

Combinatorics · Mathematics 2023-03-09 Yu-Wei Huang