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

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

2010-01-11

arxiv.org/abs/1001.1358v3

JHEP 1004:038,2010

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/JHEP04(2010)038

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.

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