Summary
Analytic properties of the partial wave amplitude for the K−+p→Σ+π reaction are investigated in the total energy space by making use of the Mandelstam representation. The unitarity condition requires the study of the pion-hyperon as well as the kaon-nucleon scattering. The latter interaction will not be important for the long-range part of the interaction, so we neglected the effect of it in this paper. The long-range part of the interaction due to the single-baryon exchange can explain the observed low-energy pion-hyperon resonances. The low-frequency of the Σ-hyperon in theI=1,p 3/2 resonance is interpreted by an accidental cancellation of the long-range potential, and hence the universality of the strong pion-baryon interaction still holds for the ΣΣπ interaction. TheI=0 andI=2,p 3/2 resonances can be interpreted by the attractive long-range interaction in the pion-hyperon scattering.
Riassunto
Facendo uso della rappresentazione di Mandelstam si studiano le proprietà analitiche dell’ampiezza d’onda parziale per la reazione K−+p→Σ+π nello spazio dell’energia totale. La condizione di unitarietà richiede lo studio dello scattering pione-iperone ed anche dello scattering kaone-nucleone. Quest’ultima interazione non è importante nella parte di lungo range dell’interazione, cosicchè in questo lavoro se ne sono trascurati gli effetti. La parte di lungo range dell’interazione, dovuta allo scambio di un solo barione, può spiegare le risonanze pione-iperone di bassa energia osservate. La bassa frequenza dell’iperone Σ nella risonanzaI=1,p 3/2 si interpreta come una eliminazione accidentale del potenziale di lungo range, e quindi la universalità delle interazioni forti pione-barione è ancora valida nell’interazione ΣΣπ. Le risonanzeI=0 e 2,p 1/2 si possono interpretare come interazioni attrattive di lungo range nello scattering pione-iperone.
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References
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Supported in part by the National Science Fondation and the Air Force Office of Scientific Research.
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Iwao, S. π− scattering in the mandelstam representation. Nuovo Cim 25, 973–994 (1962). https://doi.org/10.1007/BF02733723
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DOI: https://doi.org/10.1007/BF02733723