Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops

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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 ... continued below

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52 pages

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Bern, Zvi; /UCLA; Dixon, Lance J.; /SLAC; Smirnov, Vladimir A. & U., /Moscow State May 27, 2005.

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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.

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52 pages

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  • Journal Name: Phys.Rev.D72:085001,2005

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  • Report No.: SLAC-PUB-11210
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 890800
  • Archival Resource Key: ark:/67531/metadc874206

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  • May 27, 2005

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

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  • Nov. 29, 2016, 4:34 p.m.

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Bern, Zvi; /UCLA; Dixon, Lance J.; /SLAC; Smirnov, Vladimir A. & U., /Moscow State. Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops, article, May 27, 2005; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc874206/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.