Problems with the Quenched Approximation in the Chiral Limit

In the quenched approximation, loops of the light singlet meson (the η ′) give rise to a type of chiral logarithm absent in full QCD. These logarithms are singular in the chiral limit [1–3], 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 ¯ ψψ ∝ m −δ/(1+δ) q [3]. 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.