Quenched Chiral Perturbation Theory for Baryons

Abstract

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 $m_q^{3/2}$ is substantially altered due to the cancellation of diagrams with internal quark loops. In addition, the ${\eta }^{\prime }$ ``hairpin'' vertex leads to a new correction, proportional to $m_q^{1/2}$. We compare our results to numerical lattice data and use them to estimate the size of the quenching error in the octet baryon masses.

Comments: 7 pages (An abridged version of this note will appear in the proceedings of Lattice'93. Latex + 14 postscript files, bundled using uufiles. Needs psfig.) UW/PT-93-07