Abstract
Pion-pions andp-wave amplitudes are investigated by means of dispersion relations for the inverse partial wave amplitudes. Possible low energy zeros of thes-waves are taken into account and their positions as well as other parameters are determined by the imposition of the Balachandran-Nuyts crossing constraints and Martin's conditions and by postulating the existence of the ϱ meson. Very narrow bands of solutions are obtained, where theI=J=0 phase shifts reach 90° and thes-wave scattering lengthsa 0 vary between 0.13 and 0.23m π -1 and the ratiosa 0/a 2 between —1.8 and —3.5. It is shown that inelasticity or the passage through 180° of δ 00 near 1 GeV do not change much the predictions in the low energy region.
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Alexander von Humboldt Fellow. On leave of absence from Institut für theoretische Physik der Universität Wien.
It is a pleasure to thank Prof. M. Jacob for an interesting discussion at the beginning of this investigation and Prof. J. Wess for his kind hospitality at Karlsruhe.
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Kühnelt, H. On low energy pion-pion scattering. Z. Physik 246, 447–458 (1971). https://doi.org/10.1007/BF02115809
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DOI: https://doi.org/10.1007/BF02115809