2011/05/31 by Bo Feng, Yin Jia, Rijun Huang · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Gauge (firearms) #Gauge theory #Loop (graph theory) #Materials science #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Theoretical physics #Unitarity #hep-ph #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2011.08.024
35pages; v2:reference added and minor correction; v3; v4: to appear in NPB
arxiv created 2011/08/26 · openalex publication_date 2011/09/02 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is well known that under the color-decomposition, one-loop amplitude of gluons contains partial amplitudes of single and double trace structures, and particularly all partial amplitudes of double trace structure can be expressed as a linear combination of partial amplitudes of single trace structure. Using unitarity cut method, we prove that this result is the natural consequence of tree-level Kleiss-Kuijf relation. Generalizing the unitarity cut method to two-loop (triple cut in this case), we show that, unlike the one-loop case, partial amplitudes of double and triple trace structures can not be expressed as a linear combination of partial amplitudes of leading-color single trace structure. For partial amplitudes of subleading-color single trace structure, we have shown a very nontrivial Kleiss-Kuijf relation for six and seven-point amplitudes, which is one new result of our paper and can not be obtained by U(1)-decoupling method. Mysteriously, when we consider the case of eight points, Kleiss-Kuijf relation must be modified for subleading-color single trace partial amplitudes.