# Scattering of massless particles: scalars, gluons and gravitons

@article{Cachazo2013ScatteringOM, title={Scattering of massless particles: scalars, gluons and gravitons}, author={Freddy Cachazo and Song He and Ellis Ye Yuan}, journal={Journal of High Energy Physics}, year={2013}, volume={2014}, pages={1-33} }

A bstractIn a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U(N ) color structures while…

## 416 Citations

### Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

- Mathematics
- 2014

A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering…

### Gluons and gravitons at one loop from ambitwistor strings

- Physics
- 2017

A bstractWe present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results…

### Connected formulas for amplitudes in standard model

- Physics
- 2016

A bstractWitten’s twistor string theory has led to new representations of S-matrix in massless QFT as a single object, including Cachazo-He-Yuan formulas in general and connected formulas in four…

### Scattering equations in AdS: scalar correlators in arbitrary dimensions

- Mathematics
- 2020

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula…

### Pure gravities via color-kinematics duality for fundamental matter

- Physics
- 2014

A bstractWe give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality.…

### Scattering equations and a new factorization for amplitudes. Part I. Gauge theories

- MathematicsJournal of High Energy Physics
- 2019

A bstractIn this work we show how a double-cover (DC) extension of the Cachazo, He and Yuan formalism (CHY) can be used to provide a new realization for the factorization of the amplitudes involving…

### Fermions and the scattering equations

- Physics
- 2014

A bstractThis paper investigates how tree-level amplitudes with massless quarks, gluons and/or massless scalars transforming under a single copy of the gauge group can be expressed in the context of…

### One-loop amplitudes on the Riemann sphere

- Mathematics
- 2015

A bstractThe scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for…

### Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation

- Physics
- 2015

A bstractIn the formulation of Cachazo, He, and Yuan, tree-level amplitudes for massless particles in gauge theory and gravity can be expressed as rational functions of the Lorentz invariants ka ·…

### New formulas for amplitudes from higher-dimensional operators

- Mathematics
- 2016

A bstractIn this paper we study tree-level amplitudes from higher-dimensional operators, including F3 operator of gauge theory, and R2, R3 operators of gravity, in the Cachazo-He-Yuan formulation. As…

## References

SHOWING 1-10 OF 25 REFERENCES

### Scattering of massless particles in arbitrary dimensions.

- MathematicsPhysical review letters
- 2014

A compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions is presented and Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.

### A 'Twistor String' Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA

- Mathematics
- 2012

We propose a new formulation of the complete tree-level S-matrix of N = 8 supergravity. The new formula for n particles in the k R-charge sector is an integral over the Grassmannian G(2,n) and uses…

### Scattering in three dimensions from rational maps

- Mathematics
- 2013

A bstractThe complete tree-level S-matrix of four dimensional $ \mathcal{N}=4 $ super Yang-Mills and $ \mathcal{N}=8 $ supergravity has compact forms as integrals over the moduli space of certain…

### Gravity as the Square of Gauge Theory

- Physics
- 2010

We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged…

### On the tree level S matrix of Yang-Mills theory

- Physics
- 2004

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of…

### Residues and world sheet instantons

- Mathematics
- 2003

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance,…

### Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure

- Mathematics
- 2011

### Scattering equations and Kawai-Lewellen-Tye orthogonality

- Mathematics
- 2014

Several recent developments point to the fact that rational maps from $n$-punctured spheres to the null cone of $D$-dimensional momentum space provide a natural language for describing the scattering…

### Explicit BCJ numerators from pure spinors

- Physics
- 2011

We derive local kinematic numerators for gauge theory tree amplitudes which manifestly satisfy Jacobi identities analogous to color factors. They naturally emerge from the low energy limit of…