Summary
The problem of the asymptotic parametrization of the crossing-even forward pion-nucleon scattering amplitude is studied. A fit saturating the Froissart bound is obtained by satisfying complex-energy sum rules suggested by duality requirements in the complex energy plane in addition to the usual cross-section and real-part fitting. A comparative discussion is made of various high-energy fits of the same type obtained by different authors. Finally, the amplitude behaviour in the complex energy plane is studied, and it is found that, for fits of this kind, the extreme asymptotic limit is experimentally unattainable.
Riassunto
Si studia il problema della parametrizzazione asintotica dell’ampiezza di scattering pione-nucleone in avanti pari per incrocio. Si ottiene una formula che satura il limite di Froissart facendo uso di regole di somma a energia complessa, suggerite dal principio di dualità nel piano complesso dell’energia, in aggiunta all’abituale migliore approssimazione di sezioni d’urto e parti reali. Si fa una discussione comparativa di varie formule dello stesso tipo ottenute da diversi autori. Infine si studia il comportamento dell’ampiezza nel piano complesso dell’energia, e si trova che, per parametrizzazioni di questo tipo, il limite asintotico estremo non è raggiungibile sperimentalmente.
Реэюме
Исследуется проблема асимптотической параметриэации кроссингчетной пион-нуклонной амплитуды рассеяния вперед. Получается формула, которая насышает границу Фруассара, испольэия правила сумм для комплексной знергии, которые предполагают требования дуальности в плоскости комплексной знергии, в дополнение к подгонке поперечных сечений и вешественных частей. Проводится сравнительный аналиэ раэличных формул, полученных другими авторами. В эаключение, исследуется поведение амплитуды в плоскости комплексной знергии и получается, что для параметриэации зтого типа зкстремальный асимптотический предел является зкспериментально недостижимым.
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Ferrari, E., Lusignoli, M. Asymptotic crossing-even pion-nucleon forward scattering and duality in the complex energy plane. Nuov Cim A 23, 51–68 (1974). https://doi.org/10.1007/BF02748293
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DOI: https://doi.org/10.1007/BF02748293