Problems with the Quenched Approximation in the Chiral Limit

Abstract

In the quenched approximation, loops of the light singlet meson (the ${\eta }^{\prime }$) 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 $\cond\propto m_q^{-δ/(1+δ)}$. 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.

(talk given at Lattice '92), 4 pages latex, 3 postscript figures, uses espcr2.sty and psfig.tex (all included) UW/PT-92-20

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