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The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N} = 4$ Sudakov Form Factor

We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $ε^{-2}$ pole of the form factor using parametric integrations of finite integrals. We provide uniformly transcendental results for the master integrals through to weight six and confirm a very recent independent analytic result for the full four-loop cusp anomalous dimension of the $\mathcal{N}=4$ model.