Model independent determination of the sigma pole

Understand

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.