Evidence for hard chiral logarithms in quenched lattice QCD

We present the first direct evidence that quenched QCD differs from full QCD in the chiral (${\mathit{m}}_{\mathit{q}}$→0) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at β=6/${\mathit{g}}^2$=6.0. We measure the spectrum of light hadrons on ${16}^3$×64, ${24}^3$×64, and ${32}^3$×64 lattices, using staggered quarks of masses ${\mathit{m}}_{\mathit{q}}$=0.01, ${\mathit{m}}_{\mathit{q}}$=0.005, and ${\mathit{m}}_{\mathit{q}}$=0.0025. The pion masses show evidence for logarithmic violations of the PCAC relation ${\mathit{m}}_{\mathrm{\pi }}^2$∝${\mathit{m}}_{\mathit{q}}$, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence is seen for such chiral logarithms in the behavior of the chiral condensate 〈ψ¯ψ〉.