  The rapidity anomalous dimension controls the scaling of transverse momentum
dependent observables in the Sudakov region. In a conformal theory it is
equivalent to the soft anomalous dimension, but in QCD this relation is broken
by anomalous terms proportional to the $\beta$-function. In this paper we first
give a simple proof of this relation using two different representations of the
energy-energy correlator observable. We then calculate the anomalous terms to
three loops by computing the three-loop fully differential soft function to
$\mathcal{O}(\epsilon)$. Combined with recent perturbative data from the study
of on-shell form factors and splitting functions, this allows us to derive the
four loop rapidity anomalous dimension in QCD.
