English
Related papers

Related papers: Note on solutions of scattering equations

200 papers

One-loop scattering amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n…

High Energy Physics - Theory · Physics 2010-04-05 Mingxing Luo , Congkao Wen

The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is…

High Energy Physics - Theory · Physics 2014-01-03 Valentina Forini , Lorenzo Bianchi , Ben Hoare

We explore the space of consistent three-particle couplings in $\mathbb Z_2$-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the…

High Energy Physics - Theory · Physics 2020-01-08 Alexandre Homrich , Joao Penedones , Jonathan Toledo , Balt C. van Rees , Pedro Vieira

We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…

High Energy Physics - Theory · Physics 2023-01-04 Hongbin Chen , A. Liam Fitzpatrick , Denis Karateev

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…

High Energy Physics - Theory · Physics 2016-09-05 Michael Zlotnikov

We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely…

High Energy Physics - Theory · Physics 2011-07-22 Nima Arkani-Hamed , Freddy Cachazo , Clifford Cheung , Jared Kaplan

We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive…

Quantum Physics · Physics 2018-05-08 H. Landa

This chapter introduces the foundational elements of scattering amplitudes. It is meant to be accessible to readers with only a basic understanding of quantum field theory. Topics covered include: the four-dimensional spinor-helicity…

High Energy Physics - Theory · Physics 2023-01-10 Andreas Brandhuber , Jan Plefka , Gabriele Travaglini

In \cite{Chen:2016fgi} we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles.In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan…

High Energy Physics - Theory · Physics 2019-01-23 Gang Chen , Yeuk-Kwan E. Cheung , Tianheng Wang , Feng Xu

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…

Mathematical Physics · Physics 2011-05-10 Alexander G. Ramm

The goal of this work is threefold. First, we give an expression of the most general five point integral on M_{0,n} in terms of Chebyshev polynomials. Second, we choose a special kinematics that transforms the polynomial form of the…

High Energy Physics - Theory · Physics 2016-03-23 Carlos Cardona , Chrysostomos Kalousios

We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 T. Takenawa , M. Eguchi , B. Grammaticos , Y. Ohta , A. Ramani , J. Satsuma

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading…

High Energy Physics - Theory · Physics 2021-12-22 Jacob L. Bourjaily , Nikhil Kalyanapuram , Cameron Langer , Kokkimidis Patatoukos

The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at…

High Energy Physics - Theory · Physics 2018-09-26 Zvi Bern , Michael Enciso , Chia-Hsien Shen , Mao Zeng

We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…

Quantum Physics · Physics 2026-03-17 Roberto Bruschini

Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…

High Energy Physics - Theory · Physics 2020-02-12 Chris D. White

I study constraints on fundamental physics emerging from consistency of a unitary, local and perturbative $S$-matrix in $4d$. For massless particles, some new constraints arising from consistent complex factorisation of $2\rightarrow 2$…

High Energy Physics - Theory · Physics 2026-05-07 Timothy Trott

We study the factorization of soft and collinear singularities in dimensionally-regularized fixed-angle scattering amplitudes in massless gauge theories. Our factorization is based on replacing the hard massless partons by light-like Wilson…

High Energy Physics - Phenomenology · Physics 2009-03-19 Einan Gardi , Lorenzo Magnea

The 2 into n scattering with final particles at rest is discussed. The comparison with purely soft processes allows to identify symmetries responsible for vanishing of certain 2 into n amplitudes. Some examples are given.

High Energy Physics - Theory · Physics 2007-05-23 Joanna Domienik , Piotr Kosinski

We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…

Analysis of PDEs · Mathematics 2020-12-16 Rémi Carles , Clément Gallo