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Title: Four-loop cusp anomalous dimension from obstructions

Abstract

We introduce a method for extracting the cusp anomalous dimension at L loops from four-gluon amplitudes in N=4 Yang-Mills 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 three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop 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 four-loop 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 » variables in each term.« less

Authors:
 [1]; ;  [2]
  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9 (Canada)
  2. 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; YANG-MILLS THEORY

Citation Formats

Cachazo, Freddy, Spradlin, Marcus, and Volovich, Anastasia. Four-loop cusp anomalous dimension from obstructions. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.105011.
Cachazo, Freddy, Spradlin, Marcus, & Volovich, Anastasia. Four-loop cusp anomalous dimension from obstructions. United States. doi:10.1103/PHYSREVD.75.105011.
Cachazo, Freddy, Spradlin, Marcus, and Volovich, Anastasia. Tue . "Four-loop cusp anomalous dimension from obstructions". United States. doi:10.1103/PHYSREVD.75.105011.
@article{osti_20935270,
title = {Four-loop 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 four-gluon amplitudes in N=4 Yang-Mills 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 three-loop anomalous dimensions analytically and the four-loop one numerically. The four-loop 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 four-loop 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}
}