Experimental status of the $ππ$ 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$\to2π$ and, above all, Ke4 decays) allow a reliable, model independent determination of low energy $ππ$ 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 "$σ$ resonance" [$f_0(600)$]. We obtain the results $$a_0^{(0)}=0.233\pm0.013 M^{-1}_π,\quad b_0^{(0)}=0.285\pm0.012 M^{-3}_π$$ and, for the $σ$ pole, $$M_σ=484\pm17 \mev,\quad\gammav_σ/2= 255\pm10 {\rm MeV}.$$

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