Scattering equations and the Cachazo-He-Yuan representation for massless (and massive) gauge-theory amplitudes

Cachazo, He, and Yuan have recently unveiled a new representation for tree-level amplitudes of massless particles in various theories in terms of the solutions of a set of equations called scattering equations. This represents an alternative approach to the usual Feynman diagram decomposition of amplitudes. After reviewing the structure of tree-level gauge-theory amplitudes,  and the new CHY representation for them, we present some recent work on the extension of the CHY approach to amplitudes with massive particles.