Problems with the Quenched Approximation in the Chiral Limit

TL;DR

This paper examines the limitations of the quenched approximation in QCD, especially near the chiral limit, highlighting the presence of problematic chiral logarithms and their implications for the approximation's validity.

Contribution

The paper provides an alternative derivation using the renormalization group to show that the problematic chiral logarithms in quenched QCD cannot be simply redefined away, challenging previous assumptions.

Findings

Chiral logarithms in quenched QCD are singular in the chiral limit.

Previous summations suggested non-analytic dependencies that may be redefined.

Evidence for these effects in numerical data remains inconclusive.

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.