CHY formula and MHV amplitudes

Understand

In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions.

• We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes.
• Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes.
• This is achieved by developing techniques, in a manifestly M\"obius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants.