• DOI:10.1007/JHEP03(2017)151
• Corpus ID: 73683212

Scattering equations: real solutions and particles on a line

@article{Cachazo2016ScatteringER,
  title={Scattering equations: real solutions and particles on a line},
  author={Freddy Cachazo and Sebastian Mizera and Guojun Zhang},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2017},
  pages={1-22}
}

• F. Cachazo, Sebastian Mizera, Guojun Zhang
• Published 31 August 2016
• Mathematics
• Journal of High Energy Physics

A bstractWe find n(n − 3)/2-dimensional regions of the space of kinematic invariants, where all the solutions to the scattering equations (the core of the CHY formulation of amplitudes) for n massless particles are real. On these regions, the scattering equations are equivalent to the problem of finding stationary points of n − 3 mutually repelling particles on a finite real interval with appropriate boundary conditions. This identification directly implies that for each of the (n − 3)! possible orderings of the n − 3 particles on the interval, there exists one stable stationary point. Furthermore, restricting to four dimensions, we find that the separation of the solutions into k ∈ {2, 3, . . . , n − 2} sectors naturally matches that of permutations of n − 3 labels into those with k − 2 descents. This leads to a physical realization of the combinatorial meaning of the Eulerian numbers.