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.
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ArXiv ePrint: 1702.05840
The unusual ordering of authors instead of the standard alphabet ordering is for young researchers to get proper recognition of contributions under the current out-dated practice in China (Bo Feng).
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Huang, R., Du, YJ. & Feng, B. Understanding the cancelation of double poles in the Pfaffian of CHY-formulism. J. High Energ. Phys. 2017, 133 (2017). https://doi.org/10.1007/JHEP06(2017)133
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DOI: https://doi.org/10.1007/JHEP06(2017)133