Model independent determination of the sigma pole

TL;DR

This paper presents a model-independent method using dispersion theory to precisely determine the sigma resonance pole position from observable data, integrating lattice QCD, effective field theory, and experimental results.

Contribution

It introduces an exact formula for resonance parameters based on dispersion theory, enabling accurate, model-independent extraction of the sigma pole from experimental and lattice data.

Findings

Derived an exact formula for resonance mass and width

Applied the method to determine the sigma pole position

Analyzed error propagation in the numerical analysis

Abstract

The first part of this report reviews recent developments at the interface between lattice work on QCD with light dynamical quarks, effective field theory and low energy precision experiments. Then I discuss how dispersion theory can be used to analyze the low energy structure of the $\pi\pi$ scattering amplitude in a model independent manner. This leads to an exact formula for the mass and width of the lowest few resonances, in terms of observable quantities. As an application, I consider the pole position of the $\sigma$, paying particular to error propagation in the numerical analysis. The report is based on work done in collaboration with Irinel Caprini and Gilberto Colangelo.