Related papers: General tree-level amplitudes by factorization lim…
Using the recent formula presented by He and Cachazo-Mason-Skinner for the link representation of tree-level N=8 supergravity amplitudes, we derived a CSW-like expansion for the Next-to-MHV 6- and 7-graviton amplitudes by using the global…
In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail, in order to bridge the gap in understanding of the subject between mathematicians and physicists.…
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…
Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in…
Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with…
It is shown how tree-level multi-gluon helicity amplitudes with an arbitrary number of off-shell external gluons can be calculated via BCFW recursion. Compact expressions for helicity amplitudes for scattering processes of three and four…
We extend the recently discovered phenomenon of hidden zeros to tree amplitudes for Yang-Mills (YM) and general relativity (GR) theories with higher-derivative interactions. This includes gluon amplitudes with a single insertion of the…
Previous work on electroweak radiative corrections to high energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to…
For univariate polynomials over arbitrary field the degree gives an upper bound on the number of roots (factor theorem) and as a related result for any finite point-set one can construct a polynomial of degree equal to the cardinality…
We consider scattering amplitudes in planar N = 4 supersymmetric Yang-Mills theory in special kinematics where all external four-dimensional momenta are restricted to a (1+1)-dimensional subspace. The amplitudes are known to satisfy…
Lecture notes on Poincar\'e-invariant scattering amplitudes and tree-level recursion relations in spinor-helicity formalism. We illustrate the non-perturbative constraints imposed over on-shell amplitudes by the Lorentz Little Group, and…
Using recursion methods similar to those of Britto, Cachazo, Feng and Witten (BCFW) a direct proof of the CSW rules for computing tree-level gluon amplitudes is given.
We apply so-called tree straight-line programs to the problem of lossless compression of binary trees. We derive upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds obtained by Zhang,…
Modern on-shell S-matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for General Relativity still rely on off-shell Feynman diagram analysis. Here, we…
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…
Simon's factorization theorem is a celebrated tool in algebraic automata theory, providing bounded-depth decompositions of words with respect to morphisms into finite semigroups. We develop an analogue of Simon's theorem for \emph{forests}…
In this paper we provide detailed proofs for some of the uniqueness results presented in arXiv:1612.02797. We show that: (1) Yang-Mills and General Relativity tree-level amplitudes are completely determined by gauge invariance in $n-1$…
We analyse the high-energy behavior of tree-level graviton Compton amplitudes for particles of mass m and arbitrary spin, concentrating on a combination of forward amplitudes that will be unaffected by eventual cross- couplings to other,…
We show that a wide class of tree-level scattering amplitudes involving scalars, gauge bosons, and gravitons, up to three of which may be massive, can be expressed in terms of a Cachazo-He-Yuan representation as a sum over solutions of the…
In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for…