We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar $\mathcal{N}=4$ SYM theory, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, together with the cancellation of spurious poles, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one simple type of two-double unitarity cut. Full analytic results in terms of both symbol and Goncharov polylogarithms are provided.

• Received 24 July 2021
• Accepted 16 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.151602

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Published by the American Physical Society