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 \( \mathcal{N} \) = 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 \( \mathcal{X} \) - 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 (2)7 as a sample application.
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Golden, J., Spradlin, M. An analytic result for the two-loop seven-point MHV amplitude in \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2014, 154 (2014). https://doi.org/10.1007/JHEP08(2014)154
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DOI: https://doi.org/10.1007/JHEP08(2014)154