Advertisement

The one-loop one-mass hexagon integral in D = 6 dimensions

  • Vittorio Del Duca
  • Claude Duhr
  • Vladimir A. Smirnov
Article

Abstract

We evaluate analytically the one-loop one-mass hexagon in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three.

Keywords

Supersymmetric gauge theory QCD 

References

  1. [1]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One-loop self-dual and N =4 super Yang-Mills, Phys. Lett. B 394 (1997) 105 [hep-th/9611127] [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    V. Del Duca, C. Duhr, E.W. Nigel Glover and V.A. Smirnov, The one-loop pentagon to higher orders in epsilon, JHEP 01 (2010) 042 [arXiv:0905.0097] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    B.A. Kniehl and O.V. Tarasov, Analytic result for the one-loop scalar pentagon integral with massless propagators, Nucl. Phys. B 833 (2010) 298 [arXiv:1001.3848] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    J.M. Drummond, J.M. Henn and J. Trnka, New differential equations for on-shell loop integrals, JHEP 04 (2011) 083 [arXiv:1010.3679] [SPIRES].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    C. Anastasiou and A. Banfi, Loop lessons from Wilson loops in N =4 supersymmetric Yang-Mills theory, JHEP 02 (2011) 064 [arXiv:1101.4118] [SPIRES].ADSCrossRefMathSciNetGoogle Scholar
  7. [7]
    J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    V. Del Duca, C. Duhr and V.A. Smirnov, The massless hexagon integral in D =6 dimensions, arXiv:1104.2781 [SPIRES].
  9. [9]
    L.J. Dixon, J.M. Drummond and J.M. Henn, The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N =4 SYM, JHEP 06 (2011) 100 [arXiv:1104.2787] [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    Z. Bern et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    V. Del Duca, C. Duhr and V.A. Smirnov, An Analytic Result for the Two-Loop Hexagon Wilson Loop in N =4 SYM, JHEP 03 (2010) 099 [arXiv:0911.5332] [SPIRES].ADSCrossRefGoogle Scholar
  13. [13]
    V. Del Duca, C. Duhr and V.A. Smirnov, The Two-Loop Hexagon Wilson Loop in N =4 SYM, JHEP 05 (2010) 084 [arXiv:1003.1702] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical Polylogarithms for Amplitudes and Wilson Loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    C. Duhr, H. Gangl and J. Rhodes, Symbol calculus for polylogarithms and Feynman integrals, in preparation.Google Scholar
  16. [16]
    A.V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123 [SPIRES].MathSciNetADSGoogle Scholar
  17. [17]
    L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    H. Cheng and T.T. Wu, Expanding Protons: Scattering at High-Energies, MIT press, Cambridge U.S.A. (1987) [SPIRES].Google Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Vittorio Del Duca
    • 1
    • 2
  • Claude Duhr
    • 2
    • 3
  • Vladimir A. Smirnov
    • 4
  1. 1.INFN, Laboratori Nazionali FrascatiFrascati (Roma)Italy
  2. 2.Kavli Institute for Theoretical PhysicsSanta BarbaraU.S.A.
  3. 3.Institute for Particle Physics PhenomenologyUniversity of DurhamDurhamU.K.
  4. 4.Nuclear Physics Institute of Moscow State UniversityMoscowRussia

Personalised recommendations