A differential operator for integrating one-loop scattering equations

Understand

We propose a differential operator for computing the residues associated with a class of meromorphic $n$-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes.

• This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the $n$-form.
• We use the operator to evaluate the tree-level amplitude of $\phi^3$ theory and the one-loop integrand of Yang-Mills theory from their CHY forms.
• The method can reduce the complexity of the calculation.