Chiral logarithms in quenchedmπandfπ

A diagrammatic analysis predicts that, in the quenched approximation, there should be no chiral logarithms, at leading order, in $m_{\pi }$ or $f_{\pi }$, for gauge groups $\mathrm{SU}(N\ge 3)$. Morel has done an explicit calculation in the strong-gauge-coupling, large-dimension limit, and finds that there are such logarithms. I point out that Morel's calculation is of a quantity different from the quenched pion propagator. I show that if one calculates the correct quantity then there are no chiral logarithms. For SU(2), however, the diagrammatic analysis predicts that there are chiral logarithms in quenched $m_{\pi }$ and $f_{\pi }$.