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We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms.
D. J. Broadhurst, J. Fleischer, and O. V. Tarasov, “Two Loop Two Point Functions with Masses: Asymptotic Expansions and Taylor Series, in Any Dimension,” Z. Phys
1993
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A. B. Goncharov, “Polylogarithms and Motivic Galois Groups,” Proc. Symp. Pure Math
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A. B. Goncharov, “Multiple Polylogarithms, Cyclotomy and Modular Complexes,” Mathematical Research Letters
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J. Vollinga and S. Weinzierl, “Numerical Evaluation of Multiple Polylogarithms,” Comput. Phys. Commun
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V. A. Smirnov, Feynman Integral Calculus · 2006
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C. Duhr, “Hopf Algebras, Coproducts and Symbols: an Application to Higgs Boson Amplitudes,” JHEP
2012
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M. F. Paulos, M. Spradlin, and A. Volovich, “Mellin Amplitudes for Dual Conformal Integrals,” JHEP
2012
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S. Caron-Huot and K. J. Larsen, “Uniqueness of Two-Loop Master Contours,” JHEP
2012
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J. M. Henn, “Multiloop Integrals in Dimensional Regularization Made Simple,” Phys. Rev. Lett
2013
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2013
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2013
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A. Hodges, “The Box Integrals in Momentum-Twistor Geometry,” JHEP
2013
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M. Søgaard and Y. Zhang, “Elliptic Functions and Maximal Unitarity,” Phys. Rev
2015
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2016
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2016
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2016
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D. Broadhurst, “Feynman Integrals, L L -Series and Kloosterman Moments,” Commun. Num. Theor. Phys
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2014
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D. Simmons-Duffin, “Projectors, Shadows, and Conformal Blocks,” JHEP
2014
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2014
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2015
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2015
Cited alongside, same era.
S. Bloch and P. Vanhove, “The Elliptic Dilogarithm for the Sunset Graph,” J. Number Theory
2015
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S. Bloch, M. Kerr, and P. Vanhove, “A Feynman Integral via Higher Normal Functions,” Compos. Math
2015
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J. L. Bourjaily, L. J. Dixon, F. Dulat, and E. Panzer, “Manifestly Dual-Conformal Loop Integration,” arXiv:1801.xxxxx . Soon to appear
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2016
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2016
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2016
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J. L. Bourjaily, E. Herrmann, and J. Trnka, “Prescriptive Unitarity,” JHEP
2017
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2017
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