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Related papers: The positive geometry for $\phi^{p}$ interactions

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Tree amplitudes of the production of two kinds of scalar particles at threshold from one virtual particle are calculated in a model of two scalar fields with $O(2)$ symmetric quartic interaction and unequal masses. These amplitudes exhibit…

High Energy Physics - Phenomenology · Physics 2008-11-26 M. V. Libanov , V. A. Rubakov , S. V. Troitsky

We study remarkable connections between twistor-string formulas for tree amplitudes in ${\cal N}=4$ SYM and ${\cal N}=6$ ABJM, and the corresponding momentum amplituhedron in the kinematic space of $D=4$ and $D=3$, respectively. Based on…

High Energy Physics - Theory · Physics 2022-04-29 Song He , Chia-Kai Kuo , Yao-Qi Zhang

In \cite{arkani2018unwinding}, Arkani-Hamed, Thomas and Trnka formulated two conjectural descriptions of the tree amplituhedron $\ampli$ depending on the parity of $m$. When $m$ is even, the description involves the winding number and when…

Combinatorics · Mathematics 2023-08-23 Xavier Blot , Jian-Rong Li

The ASPIRE program, which is based on the Landau singularities and the method of power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of…

High Energy Physics - Phenomenology · Physics 2020-12-30 B. Ananthanarayan , Abhijit B. Das , Ratan Sarkar

''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain. The study of such geometries is motivated by recent…

Algebraic Geometry · Mathematics 2025-09-11 Francis Brown , Clément Dupont

In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the…

High Energy Physics - Theory · Physics 2015-05-20 Nima Arkani-Hamed , Jacob L. Bourjaily , Freddy Cachazo , Andrew Hodges , Jaroslav Trnka

We investigate numerically different techniques to extract scattering amplitudes from the Euclidean Lattice {\phi}4 theory with two fields, having different masses. We present an exploratory study of the recently proposed method by Bruno…

High Energy Physics - Lattice · Physics 2021-12-03 Marco Garofalo , Fernando Romero-López , Akaki Rusetsky , Carsten Urbach

It has recently been argued that there may be a nontrivial four-dimensional limit of the higher-dimensional Gauss--Bonnet and Lovelock interactions and that this might provide a loophole allowing for new four-dimensional gravitational…

High Energy Physics - Theory · Physics 2020-07-15 James Bonifacio , Kurt Hinterbichler , Laura A. Johnson

Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a conformal basis, for which the S-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level…

High Energy Physics - Theory · Physics 2020-01-08 Tim Adamo , Lionel Mason , Atul Sharma

Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental…

Mathematical Physics · Physics 2016-01-01 Francis Brown

The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…

Quantum Algebra · Mathematics 2024-04-16 Nick Early , Jian-Rong Li

Gauge theory amplitudes in a non-helicity format are generated at all $n$-point and at tree level. These amplitudes inherit structure from $\phi^3$ classical scattering, and the string inspired formalism is used to find the tensor algebra.…

General Physics · Physics 2007-05-23 Gordon Chalmers

We analyse the multiplicity distributions of charged particles at Tevatron (p\bar p) and LHC (pp) energies in the framework of the independent pair parton interactions (IPPI) model. It is shown that the number of soft pair parton…

High Energy Physics - Phenomenology · Physics 2015-05-28 I. M. Dremin , V. A. Nechitailo

A remarkable connection between perturbative scattering amplitudes of four-dimensional planar SYM, and the stratification of the positive grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar extension for…

High Energy Physics - Theory · Physics 2015-06-17 Yu-tin Huang , CongKao Wen

We use the recently developed massive spinor-helicity formalism [1] of Arkani- Hamed et al. to propose a new class of recursion relations for tree-level amplitudes in gauge theories. These relations are based on a combined complex…

High Energy Physics - Theory · Physics 2021-05-13 Sourav Ballav , Arkajyoti Manna

We propose a new parton model and demonstrate that the model describes the relevant experimental data at high energies. The model is based on Pomeron calculus in 1+1 space-time dimensions, as suggested in Ref. [18] and on simple assumptions…

High Energy Physics - Phenomenology · Physics 2019-03-27 E. Gotsman , E. Levin , I. Potashnikova

It has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a…

High Energy Physics - Theory · Physics 2016-03-23 Livia Ferro , Tomasz Lukowski , Andrea Orta , Matteo Parisi

Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded…

High Energy Physics - Theory · Physics 2022-03-14 Nima Arkani-Hamed , Lorenz Eberhardt , Yu-tin Huang , Sebastian Mizera

For the anisotropic $[u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]$-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic…

High Energy Physics - Theory · Physics 2009-10-28 H. Kleinert , S. Thoms

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…

Classical Analysis and ODEs · Mathematics 2017-04-13 Sabrine Arfaoui , Anouar Ben Mabrouk