Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism

Understand

For a physical field theory, the tree-level amplitudes should possess only single poles.

• However, when computing amplitudes with Cachazo-He-Yuan (CHY) formulation, individual terms in the intermediate steps will contribute higher-order poles.
• In this paper, we investigate the cancelation of higher-order poles in CHY formula with Pfaffian as the building block.
• We develop a diagrammatic rule for expanding the reduced Pfaffian.