A PCAC puzzle: π0→γγ in the σ-model

@article{Bell1969APP,
  title={A PCAC puzzle: $\pi$0→$\gamma$$\gamma$ in the $\sigma$-model},
  author={John Stewart Bell and Roman Jackiw},
  journal={Il Nuovo Cimento A (1965-1970)},
  year={1969},
  volume={60},
  pages={47-61}
}
SummaryThe 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.RiassuntoLa costante di accoppiamento effettiva per π0→γγ si dovrebbe annullare per massa del pione nulla nelle teorie con PCAC e invarianza di gauge… 
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