An Introduction to the Massive Helicity Formalism with applications to the Electroweak SM

The power of the helicity formalism has been appreciated recently from its application to the massless case, where plenty of formal aspects of multi-legs amplitudes have been derived. However, in order to extend the formalism to the realistic cases, such as the electroweak Standard Model and QCD with massive quarks, some extra inputs are needed. We discuss first the formalism needed to evaluate amplitudes expressed with the modern notation for massive fermions and vectors based on a thorough treatment of Proca vector fields. Then, we present some examples of elementary processes where it is shown how the formalism leads to tremendous simplifications, these include 2-body decays $Z\to ff$, $h\to ff$ and $h\to W^{-}{W}^{+}$ as well as the 3-body decay $h\to V{f}^{\mathrm{\prime }}\bar{f}$.