Unitarity and Unitarization

Abstract: This article reviews unitarization methods essential for extending Effective Field Theories (EFTs) beyond their perturbative limits, particularly in hadronic and electroweak (EW) sectors. Perturbative EFTs, like Chiral Perturbation Theory (ChPT), often violate unitarity bounds at higher energies, a breakdown observed in phenomena such as $ππ$ scattering resonances. To overcome this, non-perturbative techniques including the Inverse Amplitude Method (IAM), $K$-matrix formalism, and N/D approach are detailed. The IAM and the N/D methods resum perturbative series while preserving fundamental $S$-matrix principles: unitarity, analyticity, and causality, dynamically generating resonant behavior. The article emphasizes the unique role of dispersive frameworks, especially the Roy equations, which rigorously incorporate analyticity and crossing symmetry. It highlights their potential for future application in the electroweak sector, offering a powerful tool to constrain the Standard Model and interpret collider data.