Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops
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.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 890800
- Report Number(s):
- SLAC-PUB-11210; hep-th/0505205; TRN: US0604798
- Journal Information:
- Phys.Rev.D72:085001,2005, Journal Name: Phys.Rev.D72:085001,2005
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
ANOMALOUS DIMENSION
CUSPED GEOMETRIES
DIMENSIONS
FORECASTING
FORM FACTORS
GLUONS
QUANTUM CHROMODYNAMICS
QUARKS
UNITARITY
YANG-MILLS THEORY
Math and Math Physics
Phenomenology-HEP
Theory-HEP
HEPPH
HEPTH
MATH