# 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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