Quenched Chiral Perturbation Theory for Baryons

We develop chiral perturbation theory for baryons in quenched QCD. Quenching (the elimination of diagrams containing virtual quark loops) is achieved by extending the Lagrangian method of Bernard and Golterman, and is implemented in a theory where baryons are treated as fixed velocity sources. Our method requires that the octet baryons be represented by a three index tensor rather than by the usual matrix field. We calculate the leading non-analytic corrections to the masses of octet and decuplet baryons. In QCD these are proportional to $M_{\pi }^3$. We find that quenching alters the $M_{\pi }^3$ terms, but does not completely remove them. In addition, we find non-analytic contributions to baryon masses proportional to $M_{\pi }$ and $M_\pi^2 \log M_\pi$\mathrm{.}Theseterms,whichareartifactsofquenching,dominateoverthe$M_\pi^3$ terms for sufficiently small quark masses. We also point out various pecularities of the quenched theory, most notably that the $\mathrm{\Delta }$ baryon can decay (if kinematically allowed), in the sense that its two point function will be dominated at long Euclidean times by a nucleon plus pion intermediate state.