Fourloop cusp anomalous dimension from obstructions
Abstract
We introduce a method for extracting the cusp anomalous dimension at L loops from fourgluon amplitudes in N=4 YangMills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in [F. Cachazo, M. Spradlin, and A. Volovich, J. High Energy Phys. 07 (2006) 007]. We illustrate this method by extracting the two and threeloop anomalous dimensions analytically and the fourloop one numerically. The fourloop result was recently guessed to be f{sup (4)}=(4{zeta}{sub 2}{sup 3}+24{zeta}{sub 2}{zeta}{sub 4}+50{zeta}{sub 6}4(1+r){zeta}{sub 3}{sup 2}) with r=2 using integrability and string theory arguments in [N. Beisert, B. Eden, and M. Staudacher, J. Stat. Mech. (2007) P021]. Simultaneously, f{sup (4)} was computed numerically in [Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, Phys. Rev. D 75, 085010 (2007)] from the fourloop amplitude obtaining, with best precision at the symmetric point s=t, r=2.028(36). Our computation is manifestly s/t independent and improves the precision to r=2.000 02(3), providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integrationmore »
 Authors:
 Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9 (Canada)
 Brown University, Providence, Rhode Island 02912 (United States)
 Publication Date:
 OSTI Identifier:
 20935270
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105011; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANOMALOUS DIMENSION; CALCULATION METHODS; CUSPED GEOMETRIES; GLUONS; INTEGRALS; STRING MODELS; STRING THEORY; YANGMILLS THEORY
Citation Formats
Cachazo, Freddy, Spradlin, Marcus, and Volovich, Anastasia. Fourloop cusp anomalous dimension from obstructions. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.105011.
Cachazo, Freddy, Spradlin, Marcus, & Volovich, Anastasia. Fourloop cusp anomalous dimension from obstructions. United States. doi:10.1103/PHYSREVD.75.105011.
Cachazo, Freddy, Spradlin, Marcus, and Volovich, Anastasia. Tue .
"Fourloop cusp anomalous dimension from obstructions". United States.
doi:10.1103/PHYSREVD.75.105011.
@article{osti_20935270,
title = {Fourloop cusp anomalous dimension from obstructions},
author = {Cachazo, Freddy and Spradlin, Marcus and Volovich, Anastasia},
abstractNote = {We introduce a method for extracting the cusp anomalous dimension at L loops from fourgluon amplitudes in N=4 YangMills without evaluating any integrals that depend on the kinematical invariants. We show that the anomalous dimension only receives contributions from the obstructions introduced in [F. Cachazo, M. Spradlin, and A. Volovich, J. High Energy Phys. 07 (2006) 007]. We illustrate this method by extracting the two and threeloop anomalous dimensions analytically and the fourloop one numerically. The fourloop result was recently guessed to be f{sup (4)}=(4{zeta}{sub 2}{sup 3}+24{zeta}{sub 2}{zeta}{sub 4}+50{zeta}{sub 6}4(1+r){zeta}{sub 3}{sup 2}) with r=2 using integrability and string theory arguments in [N. Beisert, B. Eden, and M. Staudacher, J. Stat. Mech. (2007) P021]. Simultaneously, f{sup (4)} was computed numerically in [Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, Phys. Rev. D 75, 085010 (2007)] from the fourloop amplitude obtaining, with best precision at the symmetric point s=t, r=2.028(36). Our computation is manifestly s/t independent and improves the precision to r=2.000 02(3), providing strong evidence in favor of the conjecture. The improvement is possible due to a large reduction in the number of contributing terms, as well as a reduction in the number of integration variables in each term.},
doi = {10.1103/PHYSREVD.75.105011},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

We present an expression for the leadingcolor (planar) fourloop fourpoint amplitude of N = 4 supersymmetric YangMills theory in 42{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allowsmore »

Fourloop planar amplitude and cusp anomalous dimension in maximally supersymmetric YangMills theory
We present an expression for the leadingcolor (planar) fourloop fourpoint amplitude of N=4 supersymmetric YangMills theory in 42{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon}=0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/{epsilon}{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test amore » 
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