Freddy Cachazo

Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory

Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.

New recursion relations for tree amplitudes of gluons

Abstract We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A ( 1 + , 2 − , 3 + , 4 − , 5 + , 6 − , 7 + , 8 − ) . We show how to build any amplitude in terms of three-gluon amplitudes only.

MHV vertices and tree amplitudes in gauge theory

As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued off shell in a particular fashion. The formalism leads to new and relatively simple formulas for many amplitudes, and can be heuristically derived from twistor space.

Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills

Abstract One-loop amplitudes of gluons in N = 4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature ( − − + + ) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.

What is the simplest quantum field theory

Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory. An ever-increasing understanding of the structure of scattering amplitudes has however been pointing to the opposite conclusion. At tree level, the BCFW recursion relations that completely determine the S-matrix are valid not for scalar theories but for gauge theories and gravity, with gravitational amplitudes exhibiting the best UV behavior at infinite complex momentum. At 1-loop, amplitudes in

The all-loop integrand for scattering amplitudes in planar \mathcal{N} = 4 SYM

\mathcal{N} = 4

A duality for the S matrix

SYM only have scalar box integrals, and it was recently conjectured that the same property holds for

Scattering of Massless Particles in Arbitrary Dimensions

\mathcal{N} = 8

Scattering Amplitudes and the Positive Grassmannian

SUGRA, which plays an important role in the suspicion that this theory may be finite. In this paper we explore and extend the S-matrix paradigm, and suggest that

Scattering of massless particles: scalars, gluons and gravitons

\mathcal{N} = 8