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In this note we show that under BCFW-deformation the large z behavior of permutation sum of color-ordered gluon amplitudes found by Boels and Isermann in arxiv:1109.5888 can be simply understood from the well known Kleiss-Kuijf relation and Bern-Carrasco-Johansson relation.
R. Kleiss and H. Kuijf, “MULTI - GLUON CROSS-SECTIONS AND FIVE JET PRODUCTION AT HADRON COLLIDERS,” Nucl. Phys. B 312
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V. Del Duca, L. J. Dixon and F. Maltoni, “New color decompositions for gauge amplitudes at tree and loop level,” Nucl. Phys. B 571
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E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun. Math. Phys. 252
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R. Britto, F. Cachazo and B. Feng, “New Recursion Relations for Tree Amplitudes of Gluons,” Nucl. Phys. B 715
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R. Britto, F. Cachazo, B. Feng and E. Witten, “Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory,” Phys. Rev. Lett. 94
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P. Benincasa, C. Boucher-Veronneau and F. Cachazo, “Taming Tree Amplitudes In General Relativity,” JHEP 0711
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N. Arkani-Hamed and J. Kaplan, “On Tree Amplitudes in Gauge Theory and Gravity,” JHEP 0804
2008
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P. Benincasa and E. Conde, “Exploring the S-Matrix of Massless Particles,” arXiv:1108.3078 [hep-th]
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S. Stieberger, “Open & Closed vs. Pure Open String Disk Amplitudes,” arXiv:0907.2211 [hep-th]
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