Quenched Chiral Logarithms

TL;DR

This paper introduces a diagrammatic approach to calculate chiral logarithms in the quenched approximation, revealing specific behaviors of these logarithms in various quantities and their finite volume dependence, with some results matching numerical simulations.

Contribution

It presents a novel, physically motivated diagrammatic method for analyzing chiral logarithms in quenched QCD, including predictions for their behavior and volume dependence.

Findings

No chiral logarithms in quenched f_pi for equal u and d quark masses

Chiral logarithms in B_K are the same in quenched and full theories for m_d=m_s

Extra chiral logarithms due to eta' loops cause non-analytic quark mass dependence

Abstract

I develop a diagrammatic method for calculating chiral logarithms in the quenched approximation. While not rigorous, the method is based on physically reasonable assumptions, which can be tested by numerical simulations. The main results are that, at leading order in the chiral expansion, (a) there are no chiral logarithms in quenched $f_\pi$, for $m_u=m_d$; (b) the chiral logarithms in $B_K$ and related kaon B-parameters are, for $m_d=m_s$, the same in the quenched approximation as in the full theory; (c) for $m_\pi$ and the condensate, there are extra chiral logarithms due to loops containing the $\eta'$, which lead to a peculiar non-analytic dependence of these quantities on the bare quark mass. Following the work of Gasser and Leutwyler, I discuss how there is a predictable finite volume dependence associated with each chiral logarithm. I compare the resulting predictions with numerical results: for most quantities the expected volume dependence is smaller than the errors, but for $B_V$ and $B_A$ there is an observed dependence which is consistent with the predictions.