Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension

Understand

A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension.

• The approach is to first establish the corresponding result for massless $\phi^3$ theory using the BCFW recurrence relation and then to extend this to the gauge theory case.
• Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive $\phi^3$ theory.