Summary
We discuss the superconvergence of a certain invariant amplitude and the corrections to the Weinberg sum rules due to nonvanishing pion and kaon masses. New sum rules for spectral functions are obtained. We apply these sum rules to calculate the Kℓ3 form factors and obtain ξ=−1.54 for λ+=0 and ξ=−1.05 for λ+=0.02. These values of ξ are nearly constant throughout the physical region. These results are in very good agreement with the data of the polarization experiment.
Riassunto
Si discute la superconvergenza di una certa ampiezza invariante e le correzioni alle regole di somma di Weinberg dovute al fatto che le masse del pione e del kaone non tendono a zero. Si ottengono nuove regole di somma delle funzioni spettrali. Si applicano queste regole di somma per calcolare i fattori di forma Kℓ3 e si ottiene ξ=−1.54 per λ+=0 e ξ=−1.05 per λ+=0.02. Questi valori di ξ sono pressoché costanti in tutta la regione fisica. Questi risultati sono in ottimo accordo con i dati dell'esperimento di polarizzazione.
Резюме
Мы обсуждаем сверхсходимость некоторой инвариантной амплитуды и поправки к правилам сумм Вейнберга, обусловленные конечностью масс пиона и каона. Получаются новые правила сумм для сферических функций. Мы применяем эти правила сумм для вычисления форм-факторов Kℓ3 и получаем ξ=−1.54 для λ+=0 и ξ=−1.05 для λ+=0.02. Эти величины ξ являются почти постоянными во всей физической области. Эти результаты находятся в очень хорошем согласии с данными поляризационного эксперимента.
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Work supported in part by the U.S. Atomic Energy Commission.
Trasduzione a cura della Redazione.
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Hsu, J.P. Kℓ3 form factors and strong superconvergence. Nuovo Cimento A (1965-1970) 58, 775–782 (1968). https://doi.org/10.1007/BF02825369
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DOI: https://doi.org/10.1007/BF02825369