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Lower bounds to the π0π00π0 scattering length from unitarity, analyticity and crossing symmetry.

Нижние границы для длины π0π00π0 рассеяня, исходя из унитарности, аналитичности и кроссинт-снмметрнх.

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Il Nuovo Cimento A (1971-1996)

Summary

It is shown that for π0π00π0 scattering a rigorous lower bound to the value of the scattering amplitudeF(s, t, u) ats = 4 andt = 2 may be obtained from unitarity, analyticity and crossing symmetry. For a sufficiently smallD-wave scattering length the corresponding threshold value of the forward-scattering amplitudeF(4, 0, 0) must be greater than — 2.30 pion Compton wavelengths, which corresponds to a scattering length — 1.15.

Riassunto

Si dimostra che per lo scattering π0π00π0 si può ottenere un limite inferiore rigoroso per il valore dell’ampiezza di scatteringF(s, t, u), pers = 4 et = 2, dall’'unitarietà dall’analiticità e dalla simmetria incrociata. Per una lunghezza di scattering d’ondaD sufficientemente piccola, il valore di soglia corrispondente dell’ampiezza di scattering in avantiF(4, 0, 0) dove essere più grande di — 2.30 lunghezze d’onda del pione, il che corrisponde ad una lunghezza di scattering di — 1.15.

Резюме

Показывается, что для π0π00π0 рrассеяния строгая нижняя граница для величины амплитуды рассеянияF(s, t, u) приs = 4 qit = 2 может быть получена из унитарности, аналитичности и кроссинг-qsимметрии. Для достаточно малой длиныD волнового рассеяния соответствующее пороговое зиаче ние амплитуы рассеяния впередF(4, 0, 0) должно быть больше − 2.30 комптоновской длины волны пиона, что соответствует тлине расс∈яния − 1.15.

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Common, A.K., Wit, R. Lower bounds to the π0π00π0 scattering length from unitarity, analyticity and crossing symmetry.. Nuov Cim A 3, 179–194 (1971). https://doi.org/10.1007/BF02912616

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  • DOI: https://doi.org/10.1007/BF02912616

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