All non-maximally-helicity-violating one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory

By Z. Bern, V. Duca, L. Dixon, David A. Kosower. 2004

155 citations recorded by the source corpus.

We compute the non-MHV (non-maximally-helicity-violating) one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes (--++++) (--+-+++) (--++-++) and (-+-+-++). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n-3 positive-helicity gluons, and the color ordering (--++{center_dot}{center_dot}{center_dot}++); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d80bcb808c9ff41659a3a553a9ead8438ccbdd01

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In Nuclear and High Energy Physics

1. Kasper Risager
2. F. Cachazo
3. R. Britto
4. Bo Feng
5. Simon Badger
6. A. Brandhuber
7. G. Travaglini
8. V. Khoze

Citations in the corpus

• A direct proof of the CSW rules (2005, methodology): “ll tree amplitudes [32]. Some applications are [33, 34, 35, 36]. When using infrared concistency conditions on the one-loop amplitudes it is possible to obtain compact expressions for tree amplitudes [37, 26, 38], and this was used by the authors mentioned above to develop recursion relations [39] f”
• Non-supersymmetric loop amplitudes and MHV vertices (2004, methodology): “This coincides with one case of the general one-loop seven-gluon NMHV amplitude which was also found recently [ 12 ] using the cut-constructibility approach.”
• Tree level recursion relations in general relativity (2005, unknown): “Many of these have been obtained recently using somewhat related methods [3,4,5].”
• Direct proof of the tree-level scattering amplitude recursion relation in Yang-mills theory. (2005, background): “Many of these very compact forms have been obtained very recently [2,3,4] using somewhat related methods.”
• Recursion relations for gauge theory amplitudes with massive particles. (2005, background): “running in the loop. These contributions arise from supersymmetric theories, they are cut-constructible and largely known (at present all colour-ordered sub-amplitudes are known for AN=4 n for n ≤ 7, [32, 33, 37], and the complete Achiral N=1 n is known for n ≤ 6, [6, 7, 30, 31, 34, 35, 39, 42]). Th”
• MHV rules for Higgs plus multi-gluon amplitudes (2004, methodology): “In N = 4 SYM, the anomaly can be used to derive algebraic equations for the coefficients of integral functions [18, 19], whose solutions are in agreement with a direct evaluation of the unitary cuts for 7-gluon amplitudes [20].”
• A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix (2008, methodology): “For example, the gluonic amplitude A(1 + ,2 + ,3 g ) = [12] 3 /([23][ 31 ]) is immediately obtained by extracting the component Q 4=1 η A of (2.12).”
• Cut-constructible part of QCD amplitudes (2006, unknown): “case of next-to-MHV (NMHV) amplitudes [11,38, 26 ,28,27].”
• One-loop amplitudes of gluons in supersymmetric QCD (2005, background): “amplitudes. Using this one can easily reproduce all known results [2,3,13,14, 10 ,15] and in”
• Taming tree amplitudes in general relativity (2007, result): “ns for tree level amplitudes of gluons was introduced by Britto, Feng and the third author [7]. These recursion relations were inspired { 1 { by [8, 9] and reproduced very compact results obtained in [10] by studying the IR behavior of N= 4 one-loop amplitudes. A simple and elegant proof of the rela”
• A recursion relation for gravity amplitudes (2005, methodology): “Further progress in the calculation of one-loop amplitudes was achieved using the cutconstructibility approach [5,6] in [ 7 ], CSW diagrams [8–11], the holomorphic anomaly [12– 15] and generalized cuts [16–18].”