  We study long-distance singularities governing different physical quantities
involving massless partons in perturbative QCD by using factorisation in terms
of Wilson-line correlators. By isolating the process-independent hard-collinear
singularities from quark and gluon form factors, and identifying these with the
ones governing the elastic limit of the perturbative Parton Distribution
Functions (PDFs) -- $\delta(1-x)$ in the large-$x$ limit of DGLAP splitting
functions -- we extract the anomalous dimension controlling soft singularities
of the PDFs, verifying that it admits Casimir scaling. We then perform an
independent diagrammatic computation of the latter using its definition in
terms of Wilson lines, confirming explicitly the above result through two
loops. By comparing our eikonal PDF calculation to that of the eikonal form
factor by Erdogan and Sterman and the classical computation of the closed
parallelogram by Korchemsky and Korchemskaya, a consistent picture emerges
whereby all singularities emerge in diagrammatic configurations localised at
the cusps or along lightlike lines, but where distinct contributions to the
anomalous dimensions are associated with finite (closed) lightlike segments as
compared to infinite (open) ones. Both are relevant for resumming large
logarithms in physical quantities, notably the anomalous dimension controlling
Drell-Yan or Higgs production near threshold on the one hand, and the gluon
Regge trajectory controlling the high-energy limit of partonic scattering on
the other.
