SciPost Phys. 8, 078 (2020) ·
published 15 May 2020

· pdf
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 onshell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the highenergy 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 Lorentzcovariant formalism where polarization vectors are wellbehaved and, consequently, energy powercounting 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 treelevel order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gaugefixing functionals. It can be used to simplify Standard Model loop calculations by performing the highenergy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.
Dr Vecchi: "Below is a summary of the chan..."
in Report on Goldstone Equivalence and High Energy Electroweak Physics