Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length

Abstract

The experimental results obtained in the last few years on kaon decays (K$\to 2\pi$ and, above all, Ke4 decays) allow a reliable, model independent determination of low energy $\pi \pi$ scattering in the S0 wave. Using them and, eventually, other sets of data, it is possible to give a precise parametrization of the S0 wave as well as to find the scattering length and effective range parameter. One can also perform an extrapolation to the pole of the "$\sigma$ resonance" [$f_0(600)$]. We obtain the results $$a_0^{(0)}=0.233\pm 0.013M_{\pi }^{-1},b_0^{(0)}=0.285\pm 0.012M_{\pi }^{-3}$$ and, for the $\sigma$ pole, $$M_{\sigma }=484\pm 17\text{mev},{\text{gammav}}_{\sigma }/2=255\pm 10\mathrm{MeV}.$$

Comments: Plain TeX;4 figures; improved data used; version to appear in Phys. Rev. D