2015/12/31 by C. S. Lam, York-Peng Yao, York‐Peng Yao · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Feynman diagram #Geometry #Massless particle #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Propagator #Quantum mechanics #Scalar (mathematics) #Scattering amplitude #Sigma #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.93.105004
published as Phys. Rev. D 93, 105004 (2016) · Version to appear in Physical Review D
arxiv created 2016/04/25 · openalex publication_date 2016/05/04 · arxiv updated 2016/05/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \ensuremathσr,\ensuremathσs,\ensuremathσt, 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∞.