Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits

Abstract

We compute the three-loop contribution to the 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.

45 pages, 9 figures; v3: major revision (more stringent tests, discussion of order of limits in the Regge regime)

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Cited by in corpus (11)

• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• New differential equations for on-shell loop integrals
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Simple loop integrals and amplitudes in N=4 SYM
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• The Coulomb-branch S-matrix from massless amplitudes
• Scattering amplitudes at strong coupling for 4K gluons
• Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills