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Higgs-regularized three-loop four-gluon amplitude in \( \mathcal{N} = 4 \) SYM: exponentiation and Regge limits

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Abstract

We compute the three-loop contribution to the \( \mathcal{N} = 4 \) supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level.

We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization.

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Authors and Affiliations

  1. Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße15, 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. Brown University, Providence, Rhode Island, 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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  3. Howard J. Schnitzer
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  4. Marcus Spradlin
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Correspondence to Stephen G. Naculich.

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ArXiv ePrint: 1001.1358

Research supported in part by the NSF under grant PHY-0756518. (Stephen G. Naculich)

Research supported in part by the DOE under grant DE-FG02-92ER40706. (Howard J. Schnitzer)

Research supported in part by the DOE under grant DE-FG02-91ER40688. (Marcus Spradlin)

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Henn, J.M., Naculich, S.G., Schnitzer, H.J. et al. Higgs-regularized three-loop four-gluon amplitude in \( \mathcal{N} = 4 \) SYM: exponentiation and Regge limits. J. High Energ. Phys. 2010, 38 (2010). https://doi.org/10.1007/JHEP04(2010)038

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