Chiral logs and the quenched approximation on the lattice

The phenomenological success of the quenched approximation has been impressive in obtaining accurate results for the mass spectrum and other aspects of hadron structure. However, an independent theoretical estimate of the systematic error introduced by quenching is still missing. To this end, it can be useful to consider chiral theories which, at the one-loop level, introduced peculiar non analytical terms (the so-called chiral logs). Sharpe showed that when this framework is adapted to the quenched approximation, the dependence of the pion mass squared on the quark mass can be described by an anomalous power {dollar}delta{dollar} (the "hairpin" diagram on the pion mass shell) associated with flavor singlet loops and enhanced chiral logs. Treating the hairpin as a momentum independent mass insertion, he estimated {dollar}deltasimeq 0.2.{dollar} However, numerical calculations in quenched lattice quantum chromodynamics show little or no evidence for chiral logs at such a level.; The following work determines the anomalous power numerically by studying the pion mass as a function of the bare quark mass, as well as its volume dependence. Sources of systematic error are carefully examined. Last, the coefficient of the chiral log is calculated from the two quark-loops pion propagator. The results consistently indicate a value for the anomalous power that is approximately one order of magnitude smaller than the earlier theoretical estimate, in particular{dollar}{dollar}delta = 0.013(2){dollar}{dollar}From this one can see that for all pion masses considered, the systematic error introduced by quenching is small and always within the statistical error. Finally, by a direct calculation of the topological susceptibility of the lattice configurations, I conclude that the reason why the anomalous power is so small is a strong momentum dependence giving rise to a suppression of the hairpin at momenta comparable with the pion mass.