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 ($m_q\to 0$) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at $\beta =6\mathrm{/}{g}^2=6.0$. We measured the spectrum of light hadrons on ${16}^3\times 64$, ${24}^3\times 64$ and ${32}^3\times 64$, using staggered quarks of masses $m_q=0.01$, $m_q=0.005$ and $m_q=0.0025$. The pion masses showed clear evidence for logarithmic violations of the PCAC relation $m_{\pi }^2\propto m_q$, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate $⟨\bar{\psi }\psi ⟩$.