Quenched Chiral Perturbation Theory for Baryons

We develop quenched chiral perturbation theory for baryons using the graded-symmetry formalism of Bernard and Golterman and calculate non-analytic contributions to the baryon masses coming from quenched chiral loops. The usual term proportional to $m_q^{3\mathrm{/}2}$ is substantially altered due to the cancellation of diagrams with internal quark loops. In addition, the ${\eta }^{\mathrm{\prime }}$ ``hairpin’’ vertex leads to a new correction, proportional to $m_q^{1\mathrm{/}2}$. We compare our results to numerical lattice data and use them to estimate the size of the quenching error in the octet baryon masses.