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 KK 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