Anomalous chiral behavior in quenched lattice QCD

A study of the chiral behavior of pseudoscalar masses and decay constants is carried out in quenched lattice QCD with Wilson fermions. Using the modified quenched approximation to cure the exceptional configuration problem, accurate results are obtained for pion masses as low as $\approx 200\hspace{0.5em}\mathrm{MeV}.$ The anomalous chiral log effect associated with quenched ${\eta }^{\prime }$ loops is studied in both the relation between $m_{\pi }^2$ vs $m_q$ and in the light-mass behavior of the pseudoscalar and axial vector matrix elements. The size of these effects agrees quantitatively with a direct measurement of the ${\eta }^{\prime }$ hairpin graph, as well as with a measurement of the topological susceptibility, thus providing several independent and quantitatively consistent determinations of the quenched chiral log parameter $\delta .$ For $\beta =5.7\mathrm{}$ with clover-improved fermions ${(C}_{\mathrm{sw}}=1.57)$ all results are consistent with $\delta =0.065\mathrm{}\pm \mathrm{0.013.}$