The pion-pion scattering amplitude. II: Improved analysis above $\bar{K}K$ threshold

Abstract

We improve, in the energy region between $\bar{K}K$ threshold and $\sim 1.4$ GeV, the energy-dependent phase shift analysis of $\pi \pi$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $\pi \pi \to \bar{K}K$. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\ge 1.42$ GeV, which we also carry out. We show that this more realistic input produces $\pi \pi$ scattering amplitudes that satisfy better forward dispersion relations, particularly for ${\pi }^0{\pi }^0$ scattering.

Plain TeX. 12 figures. Minor anomaly in the K-matrix fit corrected by moving matching point to 932 MeV, and pole $M_1$ to 910.6 MeV. Results unaltered

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