Unitarity and Unitarization

TL;DR

This paper reviews unitarization techniques like IAM, K-matrix, and N/D methods that extend Effective Field Theories beyond perturbative limits, ensuring unitarity and analyticity, and discusses their applications in hadronic and electroweak physics.

Contribution

It provides a comprehensive overview of unitarization methods, emphasizing dispersive approaches like Roy equations for their rigorous incorporation of fundamental principles.

Findings

IAM and N/D methods effectively generate resonances.

Dispersive frameworks like Roy equations enhance EFT analysis.

Unitarization techniques are crucial for interpreting collider data.

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 $\pi\pi$ 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.