Summary
We present a theorem for analytic completion involving families of algebraic manifolds. As an application it is shown that the validity domain of Roy-type equations for pion-pion scattering can be extended to the range −28m 2π <s<164.7m 2π , on the basis of axiomatic analyticity. The same method applies to the enlargement of the holomorphy domain of partial-wave amplitudes.
Riassunto
Si presenta un problema per il completamento analitico che coinvolge delle famiglie di molteplicità algebriche. Come applicazione si fa vedere che si può estendere il dominio di validità di equazioni del tipo di Roy per lo scattering pione-pione all’intervallo −28m 2π <s<164.7m 2π sulla base dell’analiticità assiomatica. Lo stesso metodo si può applicare all’ampliamento del dominio di olomorfismo delle ampiezze d’onda parziale.
Реэюме
Мы предлагаем теорему для аналитического эаверщения, включаюшего семейства алгебраических множеств. Как применение зтой теоремы, покаэывается, что область применимости уравнений типа уравнений Роя для пион-пионного рассеяния может быть расщирена на область −28m 2π <s<164.7m 2π , на основе аксиоматической аналитичности. Такой же метод применяется для расщирения области голоморфности парциальных амплитуд.
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Fellow of the Consejo Nacional de Investigaciones Cientificas y Tecnicas, under CTE contract with the CEA.
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Auberson, G., Epele, L. A tool for extending the analyticity domain of partial-wave amplitudes and the validity of roy-type equations. Nuov Cim A 25, 453–466 (1975). https://doi.org/10.1007/BF02820858
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DOI: https://doi.org/10.1007/BF02820858