Finding the sigma pole by analytic extrapolation of ππ scattering data

I investigate the determination of the σ pole from ππ scattering data below the KK̄ threshold, including the new precise results obtained from Kₑ₄ decay by NA48/2 Collaboration. I discuss also the experimental status of the threshold parameters a₀⁰ and b₀⁰ and the phase shift δ₀⁰. In order to reduce the theoretical bias, I use a large class of analytic parametrizations of the isoscalar S wave, based on expansions in powers of conformal variables. The σ pole obtained with this method is consistent with the prediction based on ChPT and Roy equations. However, the theoretical uncertainties are now larger, reflecting the sensitivity of the pole position to the specific parametrizations valid in the physical region. I conclude that Roy equations offer the most precise method for the determination of the σ pole from ππ elastic scattering.