On the solutions of the scattering equations

This paper addresses the question, whether the solutions of the scattering equations in four space-time dimensions can be expressed as rational functions of the momentum twistor variables. This is the case for n ≤ 5 external particles. For general n there are always two solutions, which are rational functions of the momentum twistor variables. However, the remaining solutions are in general not rational. In the case n = 6 the remaining four solutions can be expressed as algebraic functions. These four solutions are constructed explicitly in this paper.