# Analyticity, Unitarity, Crossing: An Introduction

## Frequency

Only this year

## Summary

A fundamental subject that students workiing with scattering amplitudes and boot-straps and effective theories must know, and in order to constrain and improve theories.

## Content

Analyticity, unitarity and crossing are fundamental properties established in field theory

in the 1950s, following from locality and causality. The aim of the course would be systematically build up from first principles all the important results in the field of scattering theory, dispersion relations, as well as the results that emanate

from these general considerations.

The idea would be to give a comprehensive introduction to pion-pion scattering, analysis of form factors, and also extend some of these to pion-Kaon scattering.

Principles of rescattering are also of importance, and bring in 3 body final state effects

which could also be studied, if time permits. Important topics in these fields include

the Roy equations for pion scattering, the Roy-Steiner for pi-K, Khuri-Treiman for rescattering.

The structure of the course would be 4 lectures (2 hours each) complemented by 4 tutorial sessions (2 hour each) where one may solve problems either on the blackboard or on a Mathematica based teaching platform.

## Keywords

Pion scattering, Roy equations, form factors, dispersion relations

## Learning Prerequisites

## Recommended courses

Basic field theory, particle physics, calculus

## Learning Outcomes

By the end of the course, the student must be able to:

- Knowledge of pion scattering to tackle EFTs

## Resources

## Bibliography

Physics reports on Roy equations, several review papers, Mathematica

## Moodle Link

## Dans les plans d'études

**Forme de l'examen:**Rapport de TP (session libre)**Matière examinée:**Analyticity, Unitarity, Crossing: An Introduction**Cours:**8 Heure(s)**Exercices:**8 Heure(s)