Abstract
To first order in the pion-baryon couplings, the Feynman diagram for the decay $\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\nu}$ essentially consists of a baryon loop. By requiring it to be finite, one obtains a linear relation between the coupling constants ${g}_{\ensuremath{\pi}N}$, ${g}_{\ensuremath{\pi}\ensuremath{\Sigma}}$, and ${g}_{\ensuremath{\pi}\ensuremath{\Xi}}$. (The coupling to the $\ensuremath{\Lambda}\ensuremath{\Sigma}$ system plays no role here.) A very simple choice of values is conjectured, which produces good agreement with experiment for both the charged and neutral pion decays, when these are calculated to first order in ${g}_{\ensuremath{\pi}N}$.
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