Standard Model EFTs via on-shell methods

A bstract We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting few basics assumptions such as Poincaré invariance and locality, we classify all renormalisable non-renormalisable interactions at lowest order in couplings. From these building blocks, review how locality unitarity enforce Lie algebra structures to appear S-matrix elements together with relations among couplings (and hypercharges). Furthermore, give a fully algorithm compute any higher-point tree-level amplitude (or form factor) generic EFTs, bypassing BCFW-like recursion which are known be problematic when involved. Finally, using amplitudes techniques mixing matrix of SMEFT marginal up mass dimension 8, linear effective interactions.