Theory of resonances

TL;DR

This paper provides a comprehensive pedagogical overview of the theory of resonances, focusing on the spectrum of excited strongly interacting particles, including historical context, methodology, and applications in $S$-matrix theory and effective field theories.

Contribution

It introduces a detailed methodology for determining universal resonance parameters using the analytical properties of transition amplitudes, connecting theory with experimental data.

Findings

Summarizes the $S$-matrix theory approach to resonances

Connects resonance analysis with Effective Field Theories

Provides explicit calculations in simplified models

Abstract

We give a pedagogical introduction to the theory of resonances, focusing specifically on the spectrum of excited strongly interacting particles. After providing historical context starting from the atomic theory, we summarize the status of theoretical and experimental research. We discuss then the methodology to determine universal resonance parameter through the analytical properties of the transition amplitudes. For this, the main aspects of the $S$-matrix theory are introduced including some explicit calculations in simplified cases. In the last section, we summarize several frequently used amplitude types also making a connection to Effective Field Theories, as well as provide first glimpse into some more advanced applications to further resonance properties.