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

Abstract

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 amore » term in the three-loop quark and gluon form factors in QCD.« less

Authors:
; ;  [1]
  1. Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547 (United States)
Publication Date:
OSTI Identifier:
20713755
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 72; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.72.085001; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Bern, Zvi, Dixon, Lance J, Smirnov, Vladimir A, Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309, and Nuclear Physics Institute of Moscow State University, Moscow 119992. Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.085001.
Bern, Zvi, Dixon, Lance J, Smirnov, Vladimir A, Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309, & Nuclear Physics Institute of Moscow State University, Moscow 119992. Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond. United States. doi:10.1103/PhysRevD.72.085001.
Bern, Zvi, Dixon, Lance J, Smirnov, Vladimir A, Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309, and Nuclear Physics Institute of Moscow State University, Moscow 119992. Sat . "Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond". United States. doi:10.1103/PhysRevD.72.085001.
@article{osti_20713755,
title = {Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond},
author = {Bern, Zvi and Dixon, Lance J and Smirnov, Vladimir A and Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 and Nuclear Physics Institute of Moscow State University, Moscow 119992},
abstractNote = {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.},
doi = {10.1103/PhysRevD.72.085001},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 72,
place = {United States},
year = {2005},
month = {10}
}