Quenched Chiral Logs, the ${\eta }^{\prime }$ Mass, and the Hairpin Diagram

Abstract

Limits on the size of quenched chiral logs in the pion mass for Wilson fermions are investigated. The smallness of chiral logs is shown to be a result of the suppression of the hairpin diagram for small $p^2$, such that the value of the hairpin on the pion mass shell is much smaller than the physical $m_{{\eta }^{\prime }}^2$. A direct calculation of the topological susceptibility from the same data gives $m_{{\eta }^{\prime }}\approx 1$ GeV.