Il Nuovo Cimento A (1965-1970)

, Volume 60, Issue 1, pp 47–61 | Cite as

A PCAC puzzle: π0→γγ in the σ-model

  • J. S. Bell
  • R. Jackiw


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.


Pion Mass Surface Term Axial Current Mind Parity Auxiliary Field 
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Затруднения РСАС: π0→γγ в σ модели


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.


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.


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Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • J. S. Bell
    • 1
  • R. Jackiw
    • 1
    • 2
  1. 1.CERNGenera
  2. 2.Jefferson Laboratory of PhysicsHarvard UniversityCambridge

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