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The one-loop six-dimensional hexagon integral with three massive corners · Around

2011

The one-loop six-dimensional hexagon integral with three massive corners

Del Duca, Vittorio, Dixon, Lance J., Drummond, James M. et al.

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We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically.

After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios.
The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality.
Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol.

Built on

D. J. Broadhurst, “Summation of an infinite series of ladder diagrams,” Phys. Lett. B 307
1993
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, “One-loop self-dual and 𝒩 = 4 {\cal N}=4 super-Yang-Mills,” Phys. Lett. B 394
1997
Earlier work this paper cites.
J. M. Drummond, J. Henn, V. A. Smirnov and E. Sokatchev, “Magic identities for conformal four-point integrals,” JHEP 0701
2007
Earlier work this paper cites.

Similar

Z. Bern, L. J. Dixon, D. A. Kosower, R. Roiban, M. Spradlin, C. Vergu and A. Volovich, “The two-loop six-gluon MHV amplitude in maximally supersymmetric Yang-Mills theory,” Phys. Rev. D 78
Original
2008
Cited alongside, same era.
J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, “Hexagon Wilson loop = six-gluon MHV amplitude,” Nucl. Phys. B 815
Original
2009
Cited alongside, same era.
J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, “Dual superconformal symmetry of scattering amplitudes in 𝒩 = 4 {\cal N}=4 super-Yang-Mills theory,” Nucl. Phys. B 828
Original
2010
Cited alongside, same era.
V. Del Duca, C. Duhr and V. A. Smirnov, “An analytic result for the two-loop hexagon Wilson loop in 𝒩 = 4 {\cal N}=4 SYM,” JHEP 1003
Original
2010
Cited alongside, same era.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo and J. Trnka, “Local integrals for planar scattering amplitudes,” [arXiv:1012.6032]
Original
Cited in the paper.
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 {\cal N}=4 SYM,” [arXiv:1104.2787]
Original
Cited in the paper.
V. Del Duca, C. Duhr and V. A. Smirnov, “The massless hexagon integral in D = 6 D=6 dimensions,” [arXiv:1104.2781]
Original
Cited in the paper.
V. Del Duca, C. Duhr and V. A. Smirnov, “The one-loop one-mass hexagon integral in D = 6 D=6 dimensions,” [arXiv:1105.1333]
Original
Cited in the paper.
A. B. Goncharov, “A simple construction of Grassmannian polylogarithms,” [arXiv: 0908.2238]
Cited in the paper.
C. Duhr, H. Gangl and J. Rhodes, “Symbol calculus for polylogarithms and Feynman integrals,” in preparation
Cited in the paper.
M. Spradlin and A. Volovich, to appear
Original
Cited in the paper.

Then

V. Del Duca, C. Duhr and V. A. Smirnov, “The two-loop hexagon Wilson loop in 𝒩 = 4 {\cal N}=4 SYM,” JHEP 1005
Original
2010
Later among the works it cites.
A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, “Classical polylogarithms for amplitudes and Wilson loops,” Phys. Rev. Lett. 105
Original
2010
Later among the works it cites.
J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev, “Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes,” Nucl. Phys. B 826
Original
2010
Later among the works it cites.
J. M. Drummond, J. M. Henn and J. Trnka, “New differential equations for on-shell loop integrals,” JHEP 1104
Original
2011
Closest in time.

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