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Home > Journal of High Energy Physics (Springer/SISSA) > An analytic result for the two-loop seven-point MHV amplitude in N $$ \mathcal{N} $$ = 4 SYM |

John Golden (Department of Physics, Brown University, Box 1843, Providence, RI 02912-1843, U.S.A.) ; Marcus Spradlin (Department of Physics, Brown University, Box 1843, Providence, RI 02912-1843, U.S.A.)

29 August 2014

**Abstract: **We describe a general algorithm which builds on several pieces of data available in the literature to construct explicit analytic formulas for two-loop MHV amplitudes in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. The non-classical part of an amplitude is built from A 3 cluster polylogarithm functions; classical polylogarithms with (negative) cluster X $$ \mathcal{X} $$ - coordinate arguments are added to complete the symbol of the amplitude; beyond-the-symbol terms proportional to π 2 are determined by comparison with the differential of the amplitude; and the overall additive constant is fixed by the collinear limit. We present an explicit formula for the seven-point amplitude R 7 (2) as a sample application.

**Published in: ****JHEP 1408 (2014) 154**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP08(2014)154

**arXiv: **1406.2055

**License: **CC-BY-4.0