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More loops and legs in Higgs-regulated \( \mathcal{N} = 4 \) SYM amplitudes

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Abstract

We extend the analysis of Higgs-regulated planar amplitudes of \( \mathcal{N} = 4 \) supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine).

We also study various Regge limits of \( \mathcal{N} = 4 \) SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n ≥ 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.

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Authors and Affiliations

  1. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489, Berlin, Germany

    Johannes M. Henn

  2. Department of Physics, Bowdoin College, Brunswick, ME, 04011, U.S.A.

    Stephen G. Naculich

  3. Theoretical Physics Group, Martin Fisher School of Physics, Brandeis University, Waltham, MA, 02454, U.S.A.

    Howard J. Schnitzer

  4. Department of Physics, Brown University, Providence, RI, 02912, U.S.A.

    Marcus Spradlin

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  1. Johannes M. Henn
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  2. Stephen G. Naculich
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  4. Marcus Spradlin
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Correspondence to Stephen G. Naculich.

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ArXiv ePrint: 1004.5381

Research supported in part by the NSF under grant PHY-0756518

Research supported in part by the DOE under grant DE–FG02–92ER40706

Research supported in part by the DOE under grant DE–FG02-91ER40688

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Henn, J.M., Naculich, S.G., Schnitzer, H.J. et al. More loops and legs in Higgs-regulated \( \mathcal{N} = 4 \) SYM amplitudes. J. High Energ. Phys. 2010, 2 (2010). https://doi.org/10.1007/JHEP08(2010)002

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