Finding the sigma pole by analytic extrapolation of $ππ$ scattering data

Details Finding the sigma pole by analytic extrapolation of $ππ$ scattering data Finding the sigma pole by analytic extrapolation of $ππ$ scattering data

2008-04-22

arxiv.org/abs/0804.3504v1

Phys.Rev.D77:114019,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

Scientific paper

10.1103/PhysRevD.77.114019

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.

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