  The transition between the broken and unbroken phases of massive gauge
theories, namely the rearrangement of longitudinal and Goldstone degrees of
freedom that occurs at high energy, is not manifestly smooth in the standard
formalism. The lack of smoothness concretely shows up as an anomalous growth
with energy of the longitudinal polarization vectors, as they emerge in Feynman
rules both for real on-shell external particles and for virtual particles from
the decomposition of the gauge field propagator. This makes the
characterization of Feynman amplitudes in the high-energy limit quite
cumbersome, which in turn poses peculiar challenges in the study of Electroweak
processes at energies much above the Electroweak scale. We develop a
Lorentz-covariant formalism where polarization vectors are well-behaved and,
consequently, energy power-counting is manifest at the level of individual
Feynman diagrams. This allows us to prove the validity of the Effective W
Approximation and, more generally, the factorization of collinear emissions and
to compute the corresponding splitting functions at the tree-level order. Our
formalism applies at all orders in perturbation theory, for arbitrary gauge
groups and generic linear gauge-fixing functionals. It can be used to simplify
Standard Model loop calculations by performing the high-energy expansion
directly on the Feynman diagrams. This is illustrated by computing the
radiative corrections to the decay of the top quark.
