Showing 1 - 2 of 2 Items
More loops and legs in Higgs-regulated N = 4 SYM amplitudes
Date: 2010-01-01
Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin
Access: Open access
- We extend the analysis of Higgs-regulated planar amplitudes of 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 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. © 2010 SISSA, Trieste, Italy.
Higgs-regularized three-loop four-gluon amplitude in N = 4 SYM: Exponentiation and Regge limits
Date: 2010-01-01
Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin
Access: Open access
- 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. © SISSA 2010.