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- W2075210909 abstract "The inverse amplitude dispersion relations for pion-pion scattering including inelastic intermediate states are solved for given models of the inelastic cross section. These models are calculated by representing the four-pion intermediate state as the combination of a three-pion resonance and a single pion. Interesting results are obtained using a small and slowly varying inelastic cross section, since this leads to a resonant behavior of $R=frac{{ensuremath{sigma}}^{mathrm{tot}}}{{ensuremath{sigma}}^{mathrm{el}}}$ when the real part of the $P$-wave phase shift passes through $ensuremath{pi}$ in the inelastic region. The original solution of the pure elastic inverse amplitude equations exhibits a single sharp resonance in the $P$ wave, and the inclusion of a resonant $R$ in the iteration scheme results in the appearance of a second $P$-wave resonance. When the pion-pion coupling constant $ensuremath{lambda}ensuremath{cong}ensuremath{-}0.1$ and the three-pion decay coupling constant ${G}^{2}ensuremath{cong}1$, the positions and widths of the two di-pion resonances are ${M}_{ensuremath{zeta}}ensuremath{cong}600$ MeV, ${ensuremath{Gamma}}_{ensuremath{zeta}}ensuremath{cong}30$ MeV and ${M}_{ensuremath{rho}}ensuremath{cong}800$ MeV, ${ensuremath{Gamma}}_{ensuremath{rho}}ensuremath{cong}50$ MeV. This value of $ensuremath{lambda}$ gives $S$ waves in good agreement with independent analyses of $ensuremath{pi}ensuremath{-}N$ scattering data. These results prove that, at least for pion-pion scattering, solutions exist possessing two resonances with the same quantum numbers. When a rapidly rising inelastic cross section is used corresponding to a large ${G}^{2}$, the original elastic solution exhibiting a single $P$-wave resonance is changed inappreciably due to the dominance of the nearby inverse amplitude left cut." @default.
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- W2075210909 date "1962-10-15" @default.
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- W2075210909 title "Pion-Pion Scattering Including Inelastic Intermediate States" @default.
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- W2075210909 doi "https://doi.org/10.1103/physrev.128.859" @default.
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