The four loop QCD rapidity anomalous dimension

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