Summary
The effective coupling constant for π0→γγ should vanish for zero pion mass in theories with PCAC and gauge invariance. It does not so vanish in an explicit perturbation calculation in the σ-model. The resolution of the puzzle is effected by a modification of Pauli-Villars-Gupta regularization which respects both PCAC and gauge invariance.
Riassunto
La costante di accoppiamento effettiva per π0→γγ si dovrebbe annullare per massa del pione nulla nelle teorie con PCAC e invarianza di gauge. Non si dovrebbe verificare la stessa cosa in un esplicito calcolo perturbativo nel modello σ. Si risolve il rompicapo modificando la regolarizzazione di Pauli. Villars e Gupta, che rispetta sia la PCAC che l’invarianza di gauge.
Резюме
Зффективная константа связи для π0→γγ должна обращаться в нуль при нулевой массе пиона в теориях с РСАС и калибровочной инвариантностыо. Однако, она не обращается в нуль при точном пертурбационном вычислении в σ модели. Сазрешение зтого затруднения осуществляется лутем видоизменения регуляризации Паули-Вилларса-Гупта, которая учитывает и РСАС и калибровочную инвариантность.
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Literatur
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One of us (J.S.B.) acknowledges a very useful conversation withN. Kroll on the Gupta method.
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Bell, J.S., Jackiw, R. A PCAC puzzle: π0→γγ in the σ-model. Nuovo Cimento A (1965-1970) 60, 47–61 (1969). https://doi.org/10.1007/BF02823296
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DOI: https://doi.org/10.1007/BF02823296