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An analysis of Chew-Low integral equation

Анализ интегрального уравнения Чу-Лоу

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Il Nuovo Cimento A (1965-1970)

Summary

It has been analytically shown that the Chew-Low integral equation for the static pion-nucleon scattering problem does not have a solution for the case of no cut-off or for slowly decreasing cut-off functions. Also, for general cut-off functions, the equation can be shown to have no solution for large coupling constant. For the strong-coupling limit the new bound stateN * must have the isospin 3/2 and the spatial spin 3/2 in order to be consistent with analyticity, crossing and unitarity. The mass ofN * and the coupling constant must satisfy some equality and inequalities which are consistent with results of the strong-coupling theory.

Riassunto

È stato dimostrato analiticamente che l'equazione integrale di Chew-Low per il problema statico dello scattering pione-nucleone non ha soluzione per il caso senza taglio o per funzioni di taglio lentamente decrescenti. Si può anche dimostrare, per funzioni di taglio generali, che l'equazione non ha soluzione per grandi costanti di accoppiamento. Per il limite di forte accoppiamento il nuovo stato legatoN * deve avere l'isospin 3/2 e lo spin spaziale 3/2 per essere coerente con l'analiticità, l'incrocio e l'unitarietà. La massa delN * e la costante di accoppiamento devono soddisfare qualche uguaglianza e delle inuguaglianze che siano coerenti con i risultati della teoria dell'accoppiamento forte.

Резюме

Аналитически показано, что интегральное уравнение Чу-Лоу для проблемы статического пион-нуклонного рассеяния не имеет решения для случая необрезанных или для медленно спадающих обрезанных функций. Также, для случая общих обрезанных функций, может быть показано, что уравнение не имеет решения для больших констант связи. В пределе сильной связи новое связанное состояниеN * должно иметь изоспин 3/2 и пространственный спин 3/2 для того, чтобы удовлетворить аналитичности, кроссинг-симметрии и унитарности. МассаN * и константа связи должны удовлетворять некоторому равенству и неравенствам, которые согласуются с результатами теории сильной связи.

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Author notes

  1. S. Okubo

    Present address: Department of Physics and Astronomy, University of Rochester, 14627, Rochester, N. Y.

Authors and Affiliations

  1. Institute of Theoretical Physics, Göteborg

    S. Okubo

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To speed up publication, the author of this paper has agreed to not receive the proofs for correction.

From January to May 1973, Nordita Guest Professor.

Traduzione a cura della Redazione.

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Okubo, S. An analysis of Chew-Low integral equation. Nuov Cim A 16, 241–260 (1973). https://doi.org/10.1007/BF02819420

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