BCJ Numerators from Differential Operator of Multidimensional Residue

Understand

In previous works, we devised a differential operator for evaluating typical integrals appearing in the Cachazo-He-Yuan (CHY) forms and in this paper we further streamline this method.

• We observe that at tree level, the number of free parameters controlling the differential operator depends solely on the number of external lines, after solving the constraints arising from the scattering equations.
• This allows us to construct a reduction matrix that relates the parameters of a higher-order differential operator to those of a lower-order one.
• The reduction matrix is theory-independent and can be obtained by solving a set of explicitly given linear conditions.