Bern, Zvi; Dixon, Lance; Dunbar, David C.; Kosower, David A. One-loop \(n\)-point gauge theory amplitudes, unitarity and collinear limits. (English) Zbl 1049.81644 Nucl. Phys., B 425, No. 1-2, 217-260 (1994). Summary: We present a technique which utilizes unitarity and collinear limits to construct ansätze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution to amplitudes for n-gluon scattering in \(N=4\) supersymmetric Yang-Mills theory with the helicity configuration of the Parke-Taylor tree amplitudes. We prove that our \(N=4\) ansatz is correct using general properties of the relevant one-loop \(n\)-point integrals. We also give the “splitting amplitudes” which govern the collinear behavior of one-loop helicity amplitudes in gauge theories. Cited in 396 Documents MSC: 81T60 Supersymmetric field theories in quantum mechanics 81T15 Perturbative methods of renormalization applied to problems in quantum field theory PDFBibTeX XMLCite \textit{Z. Bern} et al., Nucl. Phys., B 425, No. 1--2, 217--260 (1994; Zbl 1049.81644) Full Text: DOI arXiv References: [1] Mangano, M.; Parke, S. J., Phys. Rep., 200, 301 (1991) [2] Parke, S. J.; Taylor, T. R., Phys. Rev. Lett., 56, 2459 (1986) [3] Berends, F. A.; Giele, W. T., Nucl. Phys., B306, 759 (1988) [4] Kosower, D. A., Nucl. Phys., B335, 23 (1990) [5] Kunszt, Z., Nucl. Phys., B271, 333 (1986) [6] Berends, F. A.; Giele, W. T., Nucl. Phys., B294, 700 (1987) [7] Kleiss, R.; Kuijf, H., Nucl. Phys., B312, 616 (1989) [8] Mangano, M.; Parke, S.; Xu, Z., Nucl. Phys., B298, 653 (1988) [9] Maxwell, C. J., Phys. Lett., B192, 190 (1987) [10] Nair, V. P., Phys. Lett., B214, 215 (1988) [11] Berends, F. A.; Giele, W. T., Nucl. Phys., B313, 595 (1989) [12] Altarelli, G.; Parisi, G., Nucl. Phys., B126, 298 (1977) [13] Bern, Z.; Dixon, L.; Kosower, D. A., Phys. Rev. Lett., 70, 2677 (1993) [14] Bern, Z.; Kosower, D. A., Nucl. Phys., B379, 451 (1993) [15] Bern, Z.; Dunbar, D. C.; Shimada, T., Phys. Lett., B312, 277 (1993) [16] Bern, Z.; Dunbar, D. C., Nucl. Phys., B379, 562 (1992) [17] Cutkosky, R. E., J. Math. Phys., 1, 429 (1960) [18] Avdeev, L. V.; Vladimirov, A. A., Nucl. Phys., B219, 262 (1983) [19] Bern, Z., (Harvey, J.; Polchinski, J., Proc. Theoretical Advanced Study Institute in High Energy Physics (TASI 92) (1993), World Scientific: World Scientific Singapore), [hep-ph/9304249] [20] Kunszt, Z.; Singer, A.; Trócsányi, Z., Nucl. Phys., B411, 397 (1994) [21] Green, M. B.; Schwarz, J. H.; Brink, L., Nucl. Phys., B198, 472 (1982) [22] Bern, Z.; Morgan, A., Phys. Rev., D49, 6155 (1994) [23] Gates, S. J.; Grisaru, M. T.; Rocek, M.; Siegel, W., Superspace, ((1983), Benjamin/Cummings: Benjamin/Cummings Menlo Park, CA), 390-391 [24] Stuart, R. G.; Gongora, A., Comput. Phys. Commun., 56, 337 (1990) [25] Aeppli, A., (PhD thesis (1992)) [26] Bern, Z.; Dixon, L.; Kosower, D. A., Nucl. Phys., B412, 751 (1994) [27] Bern, Z.; Dixon, L.; Kosower, D. A., (Halpern, M. B.; Servin, A.; Rivlis, G., Proc. Strings 1993 (1994), World Scientific: World Scientific Singapore), [hep-th/9311026] [28] Bern, Z.; Chalmers, G.; Dixon, L.; Kosower, D. A., Phys. Rev. Lett., 72, 2134 (1994), [hep-ph/9312333] [31] Mahlon, G. D., Phys. Rev., D49, 2197 (1994) [32] Del Duca, V., Phys. Rev., D48, 5133 (1993) [33] Giele, W. T.; Glover, E. W.N., Phys. Rev., D46, 1980 (1992) [34] Giele, W. T.; Glover, E. W.N.; Kosower, D. A., Nucl. Phys., B403, 633 (1993) [35] Kunszt, Z.; Soper, D., Phys. Rev., D46, 192 (1992) [37] Xu, Z.; Zhang, D.-H.; Chang, L., Nucl. Phys., B291, 392 (1987) [38] Bern, Z.; Kosower, D. A., Nucl. Phys., B362, 389 (1991) [40] Mandelstam, S., Nucl. Phys., B213, 149 (1983) [41] Mangano, M.; Parke, S. J., Nucl. Phys., B299, 673 (1988) [43] Collins, J.; Sterman, G.; Soper, D., (Mueller, A., Perturbative quantum chromodynamics (1989), World Scientific: World Scientific Singapore) [44] Furmanski, W.; Petronzio, R., Phys. Lett., B97, 437 (1980) [45] Gunion, J. F.; Kalinowski, J., Phys. Rev., D32, 2303 (1985) [46] Lewin, L., Dilogarithms and associated functions (1958), Macdonald · Zbl 0083.35904 [47] Paton, J. E.; Chan, H. M., Nucl. Phys., B10, 516 (1969) [48] Ellis, R. K.; Sexton, J. C., Nucl. Phys., B269, 445 (1986) [49] Usyukina, N. I.; Davydychev, A. I., Phys. Lett., B305, 136 (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.