The Feynman rules appear as a simple way to calculate scattering amplitudes, however some complications appear if the multiplicity of particles is large. For example, in the 2 to 2 scattering of gluons there are only 4 Feynman diagrams but if we add two extra gluons it grows to 220 diagrams. In the 80’s Stephen Parke and Tomasz Taylor found an incredible way to simplify the calculation of some classes of n-gluons scattering amplitudes based on helicity arguments. Since then, a lot of progress has been made on improving the amplitude techniques and on the understanding of the S-matrix physics. After a review of the spinor helicity formalism and some well known results based on it, I will discuss how we can use the helicity structure of scattering amplitudes in the SM and in the context of an effective Lagrangian description of BSM dynamics. The analysis reveals a novel set of helicity selection rules according to which, in the majority of 2 to 2 scattering processes at high energy, the SM and the leading BSM effects do not interfere. This have a big impact on how we should perform the EFT analysis and where we should search for new physics.
