Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data

Abstract

We investigate the determination of the $\sigma$ pole from $\pi \pi$ scattering data below the $K\bar{K}$ threshold, including the new precise results obtained from $K_{e4}$ decay by NA48/2 Collaboration. We discuss also the experimental status of the threshold parameters $a_0^0$ and $b_0^0$ and the phase shift ${\delta }_0^0$. In order to reduce the theoretical bias, we use a large class of analytic parametrizations of the isoscalar $S$-wave, based on expansions in powers of conformal variables. The $\sigma$ 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. We conclude that Roy equations offer the most precise method for the determination of the $\sigma$ pole from $\pi \pi$ elastic scattering.

References in corpus (5)

• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Model independent determination of the sigma pole
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. II. Contractions and Exact Solutions
• Theoretical progress on cusp effect and Kl4 decays
• On the determination of $\sigma$ from experimental data on the $\pi \pi$ isoscalar $S$-wave at low energies