Abstract
We study a scalar component of the 8-point next-to-next-to-maximally-helicity-violating (N2MHV) amplitude at two-loop level in \( \mathcal{N} \) = 4 super-Yang-Mills theory; it has a leading singularity proportional to the inverse of the four-mass-box square root and receives contributions from only two types of non-trivial integrals with one-loop infrared (IR) divergences. We compute such two-loop 8-point integrals by taking (double-)collinear limits of certain finite, dual-conformal-invariant integrals, and they nicely give the IR-safe ratio function after subtracting divergences. As the first genuine two-loop N2MHV amplitude computed explicitly, we find remarkable structures in its symbol and alphabet: similar to the next-to-MHV (NMHV) case, there are still 9 algebraic letters associated with the square root, and the latter also becomes a letter for the first time; unlike the NMHV case, such algebraic letters appear at either one or all of the second, third and last entry, and the part with three odd letters is particularly simple.
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He, S., Li, Z. & Zhang, C. A nice two-loop next-to-next-to-MHV amplitude in \( \mathcal{N} \) = 4 super-Yang-Mills. J. High Energ. Phys. 2022, 158 (2022). https://doi.org/10.1007/JHEP12(2022)158
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DOI: https://doi.org/10.1007/JHEP12(2022)158