Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.085001· OSTI ID:20713755

Bern, Zvi; Dixon, Lance J; Smirnov, Vladimir A ^[1]

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1. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547 (United States)

We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, as a Laurent expansion about {epsilon}=0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N=4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated Ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N=4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

• OSTI ID: 20713755
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANOMALOUS DIMENSION
FEYNMAN DIAGRAM
FORM FACTORS
GLUONS
HELICITY
ITERATIVE METHODS
QUANTUM CHROMODYNAMICS
QUARKS
SINGULARITY
SUPERSYMMETRY
UNITARITY
YANG-MILLS THEORY