More loops and legs in Higgs-regulated SYM amplitudes

• Published in: The journal of high energy physics Vol. 2010; no. 8
• Main Authors: Henn, Johannes M., Naculich, Stephen G., Schnitzer, Howard J., Spradlin, Marcus
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 02-08-2010; Springer Nature B.V
• Subjects: Amplitudes; Apexes; Classical and Quantum Gravitation; Elementary Particles; Gluons; High energy physics; Ladder diagrams; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regularization; Relativity Theory; String Theory; Yang-Mills theory; NLO Computations; AdS-CFT Correspondence; 1/N Expansion; Supersymmetric gauge theory
• ISSN: 1029-8479
• DOI: 10.1007/JHEP08(2010)002

We extend the analysis of Higgs-regulated planar amplitudes of
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
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.