Understanding the cancelation of double poles in the Pfaffian of CHY-formulism

• Main Authors: Rijun Huang, Yi-Jian Du, Bo Feng
• Format: Article
• Language: English
• Published: SpringerOpen 2017-06-01
• Series: Journal of High Energy Physics
• Subjects: Scattering Amplitudes; Gauge Symmetry
• Online Access: http://link.springer.com/article/10.1007/JHEP06(2017)133

Abstract 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. Then by organizing diagrams in appropriate groups and applying the cross-ratio identities, we show that all potential contributions to higher-order poles in the reduced Pfaffian are canceled out, i.e., only single poles survive in Yang-Mills theory and gravity. Furthermore, we show the cancelations of higher-order poles in other field theories by introducing appropriate truncations, based on the single pole structure of Pfaffian.