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

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

2007-01-04

arxiv.org/abs/hep-ph/0701025v3

Phys.Rev.D76:074034,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.76.074034

The experimental results obtained in the last few years on kaon decays (K$\to2\pi$ 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 $$a_0^{(0)}=0.233\pm0.013 M^{-1}_\pi,\quad b_0^{(0)}=0.285\pm0.012 M^{-3}_\pi$$ and, for the $\sigma$ pole, $$M_\sigma=484\pm17 \mev,\quad\gammav_\sigma/2= 255\pm10 {\rm MeV}.$$

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