Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes
Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes
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DOI：
10.1103/physrevd.93.105004
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发表时间：
2015-12
影响因子：
5
通讯作者：
C. Lam;Y. Yao
中科院分区：
文献类型：
--
作者：
C. Lam;Y. Yao
The integration over the M\"obius variables leading to the Cachazo-He-Yuan double-color $n$-point massless scalar amplitude are carried out one integral at a time. M\"obius invariance dictates the final amplitude to be independent of the three M\"obius constants ${\ensuremath{\sigma}}_{r},{\ensuremath{\sigma}}_{s},{\ensuremath{\sigma}}_{t}$, but their choice affects integrations and the intermediate results. The effect of the M\"obius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the $n\ensuremath{-}3$ integrations is explained, each exposing one of the $n\ensuremath{-}3$ propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing M\"obius constants at 0, 1, and $\ensuremath{\infty}$.
The integration over the M\"obius variables leading to the Cachazo-He-Yuan double-color $n$-point massless scalar amplitude are carried out one integral at a time. M\"obius invariance dictates the final amplitude to be independent of the three M\"obius constants ${\ensuremath{\sigma}}_{r},{\ensuremath{\sigma}}_{s},{\ensuremath{\sigma}}_{t}$, but their choice affects integrations and the intermediate results. The effect of the M\"obius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the $n\ensuremath{-}3$ integrations is explained, each exposing one of the $n\ensuremath{-}3$ propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing M\"obius constants at 0, 1, and $\ensuremath{\infty}$.