Problems with the Quenched Approximation in the Chiral Limit

Abstract

In the quenched approximation, loops of the light singlet meson (the $\eta'$) give rise to a type of chiral logarithm absent in full QCD. These logarithms are singular in the chiral limit throwing doubt upon the utility of the quenched approximation. In previous work, I summed a class of diagrams, leading to non-analytic power dependencies such as $\cond\propto m_q^{-\delta/(1+\delta)}$. I suggested, however, that these peculiar results could be redefined away. Here I give an alternative derivation of the results, based on the renormalization group, and argue that they cannot be redefined away. I discuss the evidence (or lack thereof) for such effects in numerical data.